Systems of equations with substitution: -3x-4y=-2 & y=2x-5 (video) | Khan Academy

Video transcript

so that it ‘s less probably that we get shown up by talking birds in the future, we ‘ve set a little bite of exercise for solving systems of equations with substitution. And then this is the first exercise or the first problem that they give us. -3x-4y=-2 and y=2x-5 So let me get out my little rub pad and let me rewrite the trouble. therefore this is -3x-4y=-2 and then they tell us y=2x-5. indeed, what ‘s neat about this is that they ‘ve already solved the moment equality. They ‘ve already made it explicitly solved for yttrium which makes it very easy to substitute for. We can take this constraint, the constraint on yttrium in terms of ten and substitute it for y in this inaugural blue equation and then solve for ten. So lashkar-e-taiba ‘s try it out. so this first blue equation would then become -3x-4 but alternatively of putting a y there the moment constraint tells us that y needs to be equal to 2x-5. So it ‘s 4 ( 2x-5 ) and all of that is going to be equal to -2. so now we get just one equation with one stranger. and now we precisely have to solve for ten. then, let ‘s see if we can do that. so, it ‘s -3x and then this separate right over here we have a -4, be careful, we have a -4 we want to distribute. We are going to multiply -4*2x which is -8x and -4*-5 is positive 20 and thats going to equal -2. And now we can combine all the ten terms so -3x-8x, that ‘s going to be -11x and then we have -11x+20=-2. now to solve for x, we ‘ll subtract 20 from both sides to get rid of the 20 on the left hand english. On the entrust hand side, we ‘re just left with the -11x and then on the correct hand side we are left with -22. immediately we can divide both sides by -11. And we are left with x is equal to 22 divided by 11 is 2, and the negatives cancel out. x = 2. So we are not quite done even. We ‘ve done, I guess you can say the arduous character, we have solved for x but now we have to solve for yttrium. We could take this x value to either one of these equations and solve for y. But this second one has already explicitly solved for y sol let ‘s habit that one, so it says y = 2 times and alternatively of x, we nowadays know that the x respect where these two intersect, you could view it that way is going to be equal to 2, so 2 * 2 – 5 let ‘s design out the corresponding y value. So you get y=2 ( 2 ) -5 and yttrium = 4 – 5 sol y = -1. And you can verify that it ‘ll work in this top equation If yttrium = -1 and x=2, this peak equation becomes -3 ( 2 ) which is -6-4 ( -1 ) which would be plus 4. And -6+4 is indeed -2. So it satisfies both of these equations and now we can type it in to verify that we got it right, although, we know that we did, so x=2 and y=-1. so, let ‘s type it in … x=2 and y=-1. excellent, now we ‘re much less likely to be embarassed by talking birds.

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