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Solve the system $5 x-9 y=12$ and $18 y-10 x=20$....

Question

Solve the system $5 x-9 y=12$ and $18 y-10 x=20$.

Solve the system $5 x-9 y=12$ and $18 y-10 x=20$.



Answers

Solve the system $5 x-9 y=12$ and $18 y-10 x=20$.

Yeah, this problem. We want to solve this system of equations. No exit for the three by prostitutes from something in for X. I have five times three y plus two minus 15. Wise equal to 10 distributed. My five. I have 15. Why? Plus 10 minus 15. Wise evil. It's him, 15 y minus 15 y zero. So it's just leasing 10 equals 10 which is a true statement. Since I did a true statement here, this tells me I have infinitely many solutions.

Let's solve this system with the elimination method and notice that your why terms are opposites. We have five. Why? And we have negative five. Why? So when we add those two equations together, those will cancel. They'll eliminate. So we're gonna add the ex terms Negative. Nine X plus Negative. Nine X is negative. 18 x We eliminate the white terms because five white plus negative five y zero and then we have the Constance together. Negative nine plus negative nine is negative. 18. So we have negative 18. X equals negative. 18. Let's divide both sides of that equation by negative 18 and we get X equals one. Now we need to find why. And so we're going to substitute the one into one of our two equations. So I'm going to call this equation one. And this is equation, too, so I'll substitute into Equation one, which was negative. Nine. X plus five y equals negative. Nine. I'll put the one in there for X negative. Nine times one plus five y equals negative. Nine. So this is negative. Nine plus five y equals negative nine and nine to both sides, and we get five y equals zero divide both sides of that by five. When we have Y equals zero. Now, before we write our answer, let's go ahead and do a check. And the way to check is to substitute the numbers into the second equation. So that would be negative. Nine times one minus five times zero equals negative. Nine. That would be negative. Nine minus zero equals negative. Nine that checks. So we're good. So now we read her answer as an ordered pair x comma y one comma zero.

We asked to solve for the given system of equations by Evers is substitution or elimination or the addition method. Um, but I'm going to use the addition method. And the first thing I realized is in the second equation. The X and y terms are flip flops, So I'm gonna rewrite that as negative 10 X plus eight y is equal to negative 18. So that way are variables are gonna lie. Hunger each other. So now if I almost think of this equation is being gone. Let's look at our two equations. Well, I'm gonna multiply the first equation by two because then I'll have 10 x minus eight. Y is equal to 18. And now I can add the two equations together while negative 10 x plus 10 x zero, eight y minus eight. White is also zero. So there's nothing left on the left hand side. And on the right hand side, we have negative 18 plus 18 which is zero. Well, this tells us that there's gonna be infinitely many solutions, meaning they're both the same line. So let's figure out what that Linus So I'm gonna take the first equation and solve for why so I'm going to subtract five X from both sides. So we're gonna have negative for y is equal to negative five X plus nine. Then I'm gonna divide everything by negative four, which is going to give us why equals 5/4 X minus 9/4. So what this means is every point on this line Y equals five. Force X minus sign Fourth will be a solution to that system of equation.

We're going to do problem number 85 in this question. What? We have to do a project itself away. Okay, we will solve Why in terms off X So the given aggression is five x plus May noy Is it close to 18? Ok, so let us start the converted. This is nine way Is it caused to 18 manners five x Okay, you can hurt this 18 minutes fabrics now like innovated in us 18 by nine that this to manners five by Nynex minus phi by Main X. Okay, so if you want, you can just write it in inst render form off line That is where it goes to man astray by nine x plus two or otherwise This one is also correct if you are solving for way So this becomes our solution off. Why? Ah, in a solution of why In terms off x, this becomes over Answer That is a logical stream Innisfree by nine x plus two that salt


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