Answer:
The first equation can be multiplied by 2.
Explanation:
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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Comment on eliminating y instead of x
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