Multiply the first equation −2x+y=4-2x + y = 4−2x+y=4 by 2 to align the coefficients of xxx with the second equation: 2(−2x+y)=2(4)−4x+2y=8 2(-2x + y) = 2(4) \\ -4x + 2y = 8 2(−2x+y)=2(4)−4x+2y=8
Add the modified first equation −4x+2y=8-4x + 2y = 8−4x+2y=8 to the second equation 4x−6y=−484x - 6y = -484x−6y=−48: −4x+2y+4x−6y=8+(−48)−4y=−40 -4x + 2y + 4x - 6y = 8 + (-48) \\ -4y = -40 −4x+2y+4x−6y=8+(−48)−4y=−40
Divide both sides of the equation −4y=−40-4y = -40−4y=−40 by −4-4−4 to solve for yyy: y=−40−4y=10 y = \frac{-40}{-4} \\ y = 10 y=−4−40y=10
Substitute y=10y = 10y=10 into the first equation −2x+y=4-2x + y = 4−2x+y=4: −2x+10=4−2x=4−10−2x=−6x=−6−2x=3 -2x + 10 = 4 \\ -2x = 4 - 10 \\ -2x = -6 \\ x = \frac{-6}{-2} \\ x = 3 −2x+10=4−2x=4−10−2x=−6x=−2−6x=3
x=3\boxed{x = 3}x=3 and y=10\boxed{y = 10}y=10
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