Question

solve using elimination. 7x + 6y = 10 -8x - 9y = 10

Explanation:

Step1: Eliminate y by scaling equations

To eliminate \( y \), we first find a common multiple of the coefficients of \( y \) (6 and 9), which is 18. Multiply the first equation by 3 and the second by 2:
First equation: \( 3(7x + 6y) = 3(10) \) → \( 21x + 18y = 30 \)
Second equation: \( 2(-8x - 9y) = 2(10) \) → \( -16x - 18y = 20 \)

Step2: Add the two new equations

Add the equations \( 21x + 18y = 30 \) and \( -16x - 18y = 20 \):
\( (21x - 16x) + (18y - 18y) = 30 + 20 \)
\( 5x = 50 \)

Step3: Solve for x

Divide both sides by 5:
\( x = \frac{50}{5} = 10 \)

Step4: Substitute x into first equation

Substitute \( x = 10 \) into \( 7x + 6y = 10 \):
\( 7(10) + 6y = 10 \)
\( 70 + 6y = 10 \)

Step5: Solve for y

Subtract 70 from both sides:
\( 6y = 10 - 70 = -60 \)
Divide by 6:
\( y = \frac{-60}{6} = -10 \)

Answer:

\((10, -10)\)