5

(6) For what values of a does the equation systemax+y+4z = 2 2x+y+az=2 x-3z = a...

Question

(6) For what values of a does the equation systemax+y+4z = 2 2x+y+az=2 x-3z = a

(6) For what values of a does the equation system ax+y+4z = 2 2x+y+az=2 x-3z = a



Answers

Solve each system. If a system’s equations are dependent or if there is no solution, state this. $$\begin{aligned} a \quad \quad -3 c=6 ,\\ b+2 c =2 ,\\ 7 a-3 b-5 c =14 \end{aligned}$$

38 plus five b is minus six. Five B minus a Z minus three. Let's rewrite second equation here. Put a on one side and be on the other. So a is five B plus three. Let's plug in a into the first equation here, so three into five B plus three plus five B is minus six. So 15 B plus nine plus five b is negative. Six. So 20 B plus nine is minus six. Now subtract nine on both sides. Will get 20 B minus 15. Divide by negative 50 Negative, actually, 20 on both sides, so be is minus 3/4. So we know a is five b plus three so five into minus 3/4 plus three. So it's minus 15/4 plus three. So multiply four top and bottom, so that'll be 12/4. So minus 15 uh, plus 12 that's minus three. So he's also minus 3/4

Alright. That problem is acting as to find a potential solution for a or potential answer of what they might be. So let's write out the equations just so you know, the information that we have in front of us. So we have negative nine minus a equals B and a squared minus six. A minus nine equals B. So these are the two equations we have to work with now notice they both equal be so I could set these equations equal to each other and help me solve for a right. That's what the question is asking us to do. So I'm just gonna set these equations equal to each other. So I'm gonna do negative nine minus day equals a squared minus six a minus nine. So all I did was that the equations equal to each other and now we can solve for a right. So let's go ahead and move this a over to the other side. So we'll add a on both sides. That gives us minus nine negative. Nine equals a squared negative. Six plus one is negative. Five. So we have a negative five a minus nine. Alright. Well, now let's move this nine over to the other side of the equation. So we'll add nine to both sides. Mhm and negative. Nine plus nine is zero. So we have zero equals a squared minus a squared, minus five A constantly have to deal with Now. We can keep going with this. If we wanted to, I could do zero divided by by, And I would get me zero equals a squared minus a. But the general consensus if we keep going with this, is that zero equals a. Now, If we wanted to double check our work, we could plug this a into both of these equations, right? And we would have to make sure that the bees came out to the same amount. So let's go ahead and try it. Let's go ahead and plug in a into the first equation. Negative nine minus zero is negative. Nine. So, in this case with the first equation, B equals negative nine. All right, well, let's try it with the, um, second equation, shall we? So we're gonna plug in a zero in this equation, so that leaves us with zero squared minus six time zero minus nine. Well, zero squarer zero square 20 negative six times zero is zero. So, again, that leaves us with B equals negative nine. Those two equal each other, which is exactly what we wanted according to this part of the equation. So we can conclude that a potential option for this problem to answer the question is that a equals zero.

So in this question has to find the value of A that makes this a dependent system. So first, we have three y minus two X equals zero, and we know that this is a dependent system. These need to be the same line. And then the second part we have 65 minus four X minus eight was here equal zero. I know. We need to say when is this gonna be a dependent system? So basically is gonna be zero. Because basically, when a zero, what we have here is 65 minus four acts which will be divided by two, is the same as three Y minus two acts. It's the least you become the same.

Okay, so we need to combine these on and, um come I'm using with solutions. So first things I'm going to do is I'm gonna take my third equation and my second equation. I'm gonna multiply this by three to cancel out these bees. That is when give me seven A plus c equals 20. All right, then I'm going to take this and multiply it by three. So then I can combine my first equation and this new equation. So 21 a a plus three c equals 60. So that's gonna give me 22 a equals 66. So we divide it out, we get a equals three. All right, well, I'm just gonna insert this into my first equation again. So three minus three ce equals six. Subtract three. We get three c equals three, divide out the negative one or negative three. We get C equals negative one. Okay, well, I'm going to enter this in my second equation, so I have B plus two times negative. One equals two. Well, this is the same thing that saying minus two, because this is just gonna be negative, too. And then we just switched the sounds so B minus two equals to add treatable sods. B equals four and we can double check that again by substituting for Be right here. Four months to is to sew a equals three b equals four in C equals negative one.


Similar Solved Questions

2 answers
Ercises be the set of real numbers and let X = RxR: 1La R Define. d((11,82), (y1,92)) = It1 91l + Ic2 2 . Flere (11,12) and (Y1,U2) are in X. Prove that d is & metric OE I Batric js sometimes called the taxicab metric on R:) HLa X and d be as in Exercise 1. Sketch the open ball B2 ((Q,0J6 La Ca,0] denote the set of all oathe closed continuous real valued funciue dehne bounded interval [4,6], whete & b. For f and ghe
ercises be the set of real numbers and let X = RxR: 1La R Define. d((11,82), (y1,92)) = It1 91l + Ic2 2 . Flere (11,12) and (Y1,U2) are in X. Prove that d is & metric OE I Batric js sometimes called the taxicab metric on R:) HLa X and d be as in Exercise 1. Sketch the open ball B2 ((Q,0J6 La Ca,...
5 answers
424 T When gasoline engine runs, the expanding gas product does 451 J of work pushing the piston outward the car radiator removes 325 heat from the engine_ What is the change in and_ at the same time; internal energy?
424 T When gasoline engine runs, the expanding gas product does 451 J of work pushing the piston outward the car radiator removes 325 heat from the engine_ What is the change in and_ at the same time; internal energy?...
5 answers
L Estimate Incorect. one-slded Ilmits1clcxinvou (b) limf (x) Jinf () pinor 1 49 Show1 this Question2000-201 dennuonaunb Vade 0 1f() = 46; Jorenta 'Policy
L Estimate Incorect. one-slded Ilmits 1 clcxinvou (b) limf (x) Jinf () pinor 1 49 Show 1 this Question 2000-201 denn uonaunb Vade 0 1 f() = 46 ; Jorenta 'Policy...
1 answers
LetS = {2 € R3I'T,s € R}.Verify that S is linear space; then find basis for S_ Whhat is the dimension of S?
Let S = {2 € R3I 'T,s € R}. Verify that S is linear space; then find basis for S_ Whhat is the dimension of S?...
4 answers
6. Identify the titrant in each pair that would provide a greater pH change about the equivalence point in the titration ofa 0.100 M NaOHsolution. Explain your reasoning for your choice for each pair:a) 0.10 M benzoic acid (CsHsCOzH) or 0.10 M chloroacetic acid (CICHZCHzCOzH) (2 pts)b) 0.10 M hydrofluoric acid (HF) or 0.10 Mformic acid (HCOzH) (2 pts)
6. Identify the titrant in each pair that would provide a greater pH change about the equivalence point in the titration ofa 0.100 M NaOHsolution. Explain your reasoning for your choice for each pair: a) 0.10 M benzoic acid (CsHsCOzH) or 0.10 M chloroacetic acid (CICHZCHzCOzH) (2 pts) b) 0.10 M hydr...
5 answers
Problen 2. Show that if f(r) > 0 for all r e l.6] (Uld / is integtable . then [sa Poof
Problen 2. Show that if f(r) > 0 for all r e l.6] (Uld / is integtable . then [sa Poof...
1 answers
The quark compositions of the $\mathrm{K}^{0}$ and $\Lambda^{0}$ particles are $d \bar{s}$ and uds, respectively. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for the quark constituents.
The quark compositions of the $\mathrm{K}^{0}$ and $\Lambda^{0}$ particles are $d \bar{s}$ and uds, respectively. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for the quark constituents....
1 answers
Logarithmic differentiation Use logarithmic differentiation to evaluate $f^{\prime}(x)$. $$f(x)=(2 x)^{2 x}$$
Logarithmic differentiation Use logarithmic differentiation to evaluate $f^{\prime}(x)$. $$f(x)=(2 x)^{2 x}$$...
1 answers
Draw the transition diagram of the NDFSA $M=\left(S, A, I, f, s_{0}\right),$ where: $$S=\left\{s_{0}, s_{1}, s_{2}, s_{3}\right\}, A=\left\{s_{2}\right\}$$ TABLE CANNOT COPY
Draw the transition diagram of the NDFSA $M=\left(S, A, I, f, s_{0}\right),$ where: $$S=\left\{s_{0}, s_{1}, s_{2}, s_{3}\right\}, A=\left\{s_{2}\right\}$$ TABLE CANNOT COPY...
5 answers
Integrate the following:sinb (x)cos(x)dxb)Sp dtc)x(5 x2)2dx
Integrate the following: sinb (x)cos(x)dx b) Sp dt c) x(5 x2)2dx...
5 answers
Find the area in the first quadrant bounded by y=1/(x^2+1) and the coordinate axis
find the area in the first quadrant bounded by y= 1/(x^2+1) and the coordinate axis...
5 answers
Point) The coetilclent Of determlnation coufficlent ot the data answt:data polnts Oodand the slope of Ihe regress on Iine Is -4.42. Datermina the Inear conelation
point) The coetilclent Of determlnation coufficlent ot the data answt: data polnts Oodand the slope of Ihe regress on Iine Is -4.42. Datermina the Inear conelation...
5 answers
For the function f(z) 3 6ez calculate the following function values: f( _ 3) =f( _ 1) = f(0) = f(1) = f(3)
For the function f(z) 3 6ez calculate the following function values: f( _ 3) = f( _ 1) = f(0) = f(1) = f(3)...
5 answers
Find the indefinite integral: (Use € for the constant of integration ) sin X dx coS
Find the indefinite integral: (Use € for the constant of integration ) sin X dx coS...
5 answers
Caceen4For anacid HA witha PK,0f9.2, what is the ratioof the conjugate base to theacid at pH7.2 for the following two condi tions: total concentrations of HA being C 0.0042 Mand 0.00042 M?
Caceen4 For anacid HA witha PK,0f9.2, what is the ratioof the conjugate base to theacid at pH7.2 for the following two condi tions: total concentrations of HA being C 0.0042 Mand 0.00042 M?...

-- 0.020185--