Question

solve the system of equations. 11x + 4y = -46 7x - 4y = 10 x = y =

Explanation:

Step1: Add the two equations to eliminate \( y \)

The two equations are:
\( 11x + 4y = -46 \)
\( 7x - 4y = 10 \)

Adding them together: \( (11x + 4y) + (7x - 4y) = -46 + 10 \)
Simplify the left side: \( 11x + 7x + 4y - 4y = 18x \)
Simplify the right side: \( -36 \)
So we have \( 18x = -36 \)

Step2: Solve for \( x \)

Divide both sides of \( 18x = -36 \) by 18: \( x = \frac{-36}{18} = -2 \)

Step3: Substitute \( x = -2 \) into one of the original equations to find \( y \)

Let's use the second equation \( 7x - 4y = 10 \)
Substitute \( x = -2 \): \( 7(-2) - 4y = 10 \)
Calculate \( 7(-2) \): \( -14 - 4y = 10 \)

Step4: Solve for \( y \)

Add 14 to both sides: \( -4y = 10 + 14 = 24 \)
Divide both sides by -4: \( y = \frac{24}{-4} = -6 \)

Answer:

\( x = -2 \)
\( y = -6 \)