And you can verify that it'll work in this top equation If y = -1 and x=2, this top equation becomes -3(2) which is -6-4(-1) which would be plus 4. But this second one has already explicitly solved for y so let's use that one, so it says y = 2 times and instead of x, we now know that the x value where these two intersect, you could view it that way is going to be equal to 2, so 2 * 2 - 5 let's figure out the corresponding y value. We could take this x value to either one of these equations and solve for y. We've done, I guess you can say the hard part, we have solved for x but now we have to solve for y. And we are left with x is equal to 22 divided by 11 is 2, and the negatives cancel out. On the left hand side, we're just left with the -11x and then on the right hand side we are left with -22. Now to solve for x, we'll subtract 20 from both sides to get rid of the 20 on the left hand side. And now we can combine all the x terms so -3x-8x, that's going to be -11x and then we have -11x+20=-2. We are going to multiply -4*2x which is -8x and -4*-5 is positive 20 and thats going to equal -2.

So, it's -3x and then this part right over here we have a -4, be careful, we have a -4 we want to distribute. So now we get just one equation with one unknown. So it's 4(2x-5) and all of that is going to be equal to -2. So this first blue equation would then become -3x-4 but instead of putting a y there the second constraint tells us that y needs to be equal to 2x-5. We can take this constraint, the constraint on y in terms of x and substitute it for y in this first blue equation and then solve for x. They've already made it explicitly solved for y which makes it very easy to substitute for.

So, what's neat about this is that they've already solved the second equation. So this is -3x-4y=-2 and then they tell us y=2x-5. 3x-4y=-2 and y=2x-5 So let me get out my little scratch pad and let me rewrite the problem. And so this is the first exercise or the first problem that they give us.

So that it's less likely that we get shown up by talking birds in the future, we've set a little bit of exercise for solving systems of equations with substitution.

Solving systems of equations