Answer: x = 0 y = -1
Explanation:
To solve by elimination, multiply the first equation by 4 , then add the two equations
(4)(2x + 5y = -5) becomes
8x +20y = -20
-8x -1y = 1 becomes
0 + 19y = -19 divide both sides by 19
y = -1 Substitute -1 for y in either equation, then solve for x
2x + 5( -1) = -5 Distribute
2x -5 = -5 Add 5 to both sides
2x +5 -5 = -5 + 5 Combine like terms.
2x = 0
Check: 2x + 5y = -5 is 2(0) = 5(-1) = -5
0 + -5 = -5 True
-8x -1y = 1 is -8(0) -1(-1) = 1
0 + 1 = 1 True
OR
To solve by substitution, rewrite the second equation to isolate y.
-8x -1y = 1 Add 8x to both sides
-1y = 8x + 1 Multiply both sides by -1
y = -8x -1 Substitute (-8x -1) in place of y in the first equation.
2x + 5y = -5 becomes
2x + 5(-8x -1) = -5 Distribute and rewrite
2x - 40x -5 = -5 Add 5 to both sides
2x - 40x -5 = -5 + 5 Combine like terms.
-38x = 0 To Solve for x, Divide both sides by -38 (Actually unnecessary!)
x = 0 Substitute this value for x in the second equation and solve for y
-8(0) -1y = 1
0 - y = 1
-y = 1 Multiply both sides by -1 (reverse signs)
y = -1