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Solve algebraically: $quad 4 mathrm{x}+2 mathrm{y}=-1$ $5 x-3 y=7$...

Question

Solve algebraically: $quad 4 mathrm{x}+2 mathrm{y}=-1$ $5 x-3 y=7$

Solve algebraically: $quad 4 mathrm{x}+2 mathrm{y}=-1$ $5 x-3 y=7$



Answers

Solve each system of equations.

$$
\begin{array}{l}{4 x+y=7} \\ {3 x+\frac{4}{5} y=5.5}\end{array}
$$

So in this costume warehouse to solve the given system by substitution, which means we're basically gonna be isolating one very look. And first, all right down are given assistant before I expose to wipe all seven. And then we have white was five. So basically a dis question. You've already been given an isolator. Why was five acts? It's not just finding this value for why, which is five X back is displeased. So we end up with four expose tennis, equal seven, and basically we just crossed out this wine, made it fight. If we saw this out, we get X equals one because 14 x equal stuff. It's not your value for axe identifying why we could just put this back in right here like equals five times 1/2 of five on the chip. Now I have a solution, which is 1/2 5 over to X is 1/2 wives, 52

So we're asked to solve the system of equations using either substitution or elimination. So I'm gonna choose to use substitution because we're given a wide variable alone here so we can work with that pretty easily. So the first thing I'm gonna do is subtract three extra both sides of this equation. Just gonna turn into why is equal to four minus three acts and two acts minus for why is he going to seven our next step? It's a substitute in Why's He Will do four minus three acts into the second equation, which yields to acts minus four times four minus three acts is equal to seven and that why is equal to four minus three X? Our next step is in the second equation to go ahead and solve for acts. If we go ahead and we simplify this first are the left hand side of the equation. We get that wise you could do floor minus three x and that 14 Excuse me 14 X minus 16 to go to seven. Let's go ahead and solve that for axe and we get, um, well, yet X is equal to 23 over 14. And why is it illegal to four minus three acts. Great. So our last step is to go ahead and substituting. We have for acts, right? They're pretty cool. If we go ahead and do that, we're going to say what is four minus three times 23 over 14? Well, that is X is equal to 23 over 14. Great. And why is equal to negative 13 over 14? Perfect. And this is our final answer is that X is equal to 23 over 14 and wise it with negative 30.

Hello. Today's problem is a linear systems system of linear equations. Problem where we need to solve this system by using the elimination method. So when I look at the problem itself, I see the exes. We could work with that. But when I look at the wise, I see we have negative seven y and negative seven. Why? So if we could just change one of these to a positive seven? Why, that's gonna allow us to, um, that's gonna allow us to eliminate Why has a variable pretty easily. And so to do that, I'm gonna multiply this bottom equation by negative one, because that's gonna get rid of some of these negatives for me. Okay, Now, when I do that, what I like you like to do I like to rewrite my equation. Um, the 1st 1 since I'm not I don't need to change the 1st 1 at all, so I'm just gonna rewrite it over here, and then the 2nd 1 I need to multiply this negative one. I need to distribute it or multiply every term by negative one. Okay, So negative one times X is gonna be negative. One x uh, negative one times negative seven lives plus seven y. And that's the key. Because now these two are opposites, which is what we want. And the negative one times negative 15 is going to be positive. 15. And so when I add these together, if I use red here, we're gonna add these together. Four X plus one access three X equals cause seven negative seven y, and seven why are equal zero and three plus 15 is 18. I can divide both sides by three, and I end up with X is equal to six. Okay, now I take that, uh, X equal six. I'm not done yet. I need to substitute that back into one of my equations up here. It doesn't matter which one of these I used. It's just a matter of preference. Sometimes you see something that makes it a little, um, the math a little simpler. I guess they're more efficient, but I'm just going to use this top one right here. Um, I don't know. Just because it's on the top, I guess. No real reason. Uh, before times six, I'm substituting the six right here in for X subtract seven. Y equals three. Four times six is 24. Subtract seven y equals three. I have to subtract 24 on both sides. Um, I'll be careful here that negative seven. Why that the negative seven drops down? That's a common air right there. And three subtract 24 is negative. 21 and then and last up. Um, now you're seven times why the inverse of multiplication is division. So I end up with why is equal to native 21 divided by negative seven is actually going to be positive. Three. And if I have to write my answer as an ordered pair, the point on the graph where these two lines would cross would be at the 20.63 Uh, thanks for what?


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