Question

solve the following system of equations.
-5x - 2y = 23
4x + 9y = -11
x =

y =

Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 9 and the second by 2 to make coefficients of y opposite.
First equation: $-5x - 2y = 23$ $\times 9$: $-45x - 18y = 207$
Second equation: $4x + 9y = -11$ $\times 2$: $8x + 18y = -22$

Step2: Add the two new equations

Add $-45x - 18y = 207$ and $8x + 18y = -22$:
$(-45x + 8x) + (-18y + 18y) = 207 + (-22)$
$-37x = 185$

Step3: Solve for x

Divide both sides by -37:
$x = \frac{185}{-37} = -5$

Step4: Substitute x = -5 into one of the original equations (e.g., 4x + 9y = -11)

$4(-5) + 9y = -11$
$-20 + 9y = -11$

Step5: Solve for y

Add 20 to both sides: $9y = -11 + 20 = 9$
Divide by 9: $y = \frac{9}{9} = 1$

Answer:

$x = -5$, $y = 1$