The x-coefficients are -2 and 4. If the first one of these is multiplied by 2, it will be the opposite of the second of these. That is 2·(-2) = -4. When -4 and 4 are added, the result is 0, so the x-variable will be eliminated.

To solve these equations by "elimination", you look for simple relationships between the coefficients that will let you combine them to get zero.

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Here's the rest of the solution.

2(-2x-5y) +(4x+2y) = 2(-1) +(8) . . . . after multiplying the first equation by 2 and adding the second equation

-4x -10y +4x +2y = -2 +8 . . . . . the result of eliminating parentheses

-8y = 6 . . . . . the result of collecting terms

y = -6/8 = -3/4 . . . . divide by the y-coefficient

Since all of the coefficients in the second equation are even, a factor of 2 can be removed, and the equation written as ...

2x +y = 4

This can be solved for x, so you have ...

x = (4 -y)/2 = 2 -(y/2)

Filling in the above value of y, we find x to be ...

x = 2 -(-3/4)/2

x = 2 3/8

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<em>Comment on eliminating y instead of x</em>

If you divide the second equation by 2 so that y has a coefficient of 1, then you can multiply this equation by 5 to give y a coefficient that is the opposite of the coefficient -5 in the first equation. Then the elimination looks like

(-2x -5y) +5(2x +y) = (-1) +5(4)

-2x -5y +10x +5y = -1 +20 . . . . eliminate parentheses

8x = 19 . . . . simplify

x = 19/8 = 2 3/8 . . . . divide by the coefficient of x

5 0

3 years ago