Question

solve the system of equations -2x - y = -4 and 7x + 8y = 41 by combining the equations.

Explanation:

Step1: Label the equations

Let the first equation be \( -2x - y = -4 \) (Equation 1) and the second equation be \( 7x + 8y = 41 \) (Equation 2).

Step2: Multiply Equation 1 by 8

To eliminate \( y \), we multiply Equation 1 by 8.
\( 8\times(-2x - y)=8\times(-4) \)
\( -16x - 8y = -32 \) (Equation 3)

Step3: Add Equation 2 and Equation 3

Add Equation 2 (\( 7x + 8y = 41 \)) and Equation 3 (\( -16x - 8y = -32 \)):
\( (7x - 16x)+(8y - 8y)=41 - 32 \)
\( -9x = 9 \)

Step4: Solve for \( x \)

Divide both sides by -9:
\( x=\frac{9}{-9}=-1 \)

Step5: Substitute \( x = -1 \) into Equation 1

Substitute \( x=-1 \) into \( -2x - y = -4 \):
\( -2\times(-1)-y=-4 \)
\( 2 - y = -4 \)

Step6: Solve for \( y \)

Subtract 2 from both sides:
\( -y=-4 - 2=-6 \)
Multiply both sides by -1:
\( y = 6 \)

Answer:

The solution to the system is \( x=-1 \), \( y = 6 \)