How do you solve x + y =1x+y=1 and 2x-y=-22x−y=−2 using substitution?

1 Answer
Alexander
Jul 10, 2016

By eliminating xx in the expression x+y=1x+y=1, we get

x = 1-yx=1−y, which we can plug in the second expression:

2(1-y)-y=-22(1−y)−y=−2

2-2y-y=-22−2y−y=−2

2-3y=-22−3y=−2

-3y+2=-2−3y+2=−2

-3y=-4−3y=−4

y=4/3y=43

Knowing yy, we can now find xx by plugging the yy-value into any of the above equations. For example, by plugging y=4y=4 into the first equation, x+y=1x+y=1, we get

x+4/3=1x+43=1

x=-1/3x=−13

Explanation:

We can check whether these values satisfy the equations by plugging them back in:

First: x+y=1x+y=1

-1/3 + 4/3 = 1 -> 4/3-1/3 = 1 -> (12-3)/(9) = 1 -> 9/9 = 1−13+43=1→43−13=1→12−39=1→99=1

Second: 2x-y=-22x−y=−2

2(-1/3)-4/3=-2 -> -2/3-4/3 = -2 -> -18/9 = -22(−13)−43=−2→−23−43=−2→−189=−2

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