Question

solve this system of equations using the elimination method.
-12x - 3y = -30
6x + 9y = 0
show your work
find your answer below and give your deer the corresponding tail.
(2, 2)
(3, -2)
(1, 6)
(3, 2)

Explanation:

Step1: Label the equations

Let the first equation be \( -12x - 3y = -30 \) (Equation 1) and the second equation be \( 6x + 9y = 0 \) (Equation 2).

Step2: Eliminate x

Multiply Equation 2 by 2 to make the coefficients of x opposite:
\( 2\times(6x + 9y) = 2\times0 \)
\( 12x + 18y = 0 \) (Equation 3)

Step3: Add Equation 1 and Equation 3

\( (-12x - 3y) + (12x + 18y) = -30 + 0 \)
Simplify: \( 15y = -30 \)

Step4: Solve for y

Divide both sides by 15: \( y = \frac{-30}{15} = -2 \)

Step5: Substitute y into Equation 2

\( 6x + 9(-2) = 0 \)
\( 6x - 18 = 0 \)
Add 18 to both sides: \( 6x = 18 \)
Divide by 6: \( x = 3 \)

Answer:

The solution is \( (3, -2) \)