![]() 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.
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