Questions: Solve the system of equations -2x+y=4 and 4x-6y=-48 by combining the equations.

Solve the system of equations -2x+y=4 and 4x-6y=-48 by combining the equations.
Transcript text: Solve the system of equations $-2 x+y=4$ and $4 x-6 y=-48$ by combining the equations.
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Solution

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Solution Steps

Step 1: Multiply the first equation to align coefficients

Multiply the first equation 2x+y=4-2x + y = 4 by 2 to align the coefficients of xx with the second equation: 2(2x+y)=2(4)4x+2y=8 2(-2x + y) = 2(4) \\ -4x + 2y = 8

Step 2: Add the modified first equation to the second equation

Add the modified first equation 4x+2y=8-4x + 2y = 8 to the second equation 4x6y=484x - 6y = -48: 4x+2y+4x6y=8+(48)4y=40 -4x + 2y + 4x - 6y = 8 + (-48) \\ -4y = -40

Step 3: Solve for yy

Divide both sides of the equation 4y=40-4y = -40 by 4-4 to solve for yy: y=404y=10 y = \frac{-40}{-4} \\ y = 10

Step 4: Substitute yy back into the first equation to solve for xx

Substitute y=10y = 10 into the first equation 2x+y=4-2x + y = 4: 2x+10=42x=4102x=6x=62x=3 -2x + 10 = 4 \\ -2x = 4 - 10 \\ -2x = -6 \\ x = \frac{-6}{-2} \\ x = 3

Final Answer

x=3\boxed{x = 3} and y=10\boxed{y = 10}

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