Questions: 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.

Solution

Step 1: Multiply the first equation to align coefficients

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

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

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

Step 3: Solve for $y$

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

Step 4: Substitute $y$ back into the first equation to solve for $x$

Substitute $y = 10$ into the first equation $-2x + y = 4$: \[ -2x + 10 = 4 \\ -2x = 4 - 10 \\ -2x = -6 \\ x = \frac{-6}{-2} \\ x = 3 \]

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

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