Question

solve using elimination.
-10x + 10y = 20
9x - 10y = -10
(\boxed{\quad}, \boxed{\quad})

Explanation:

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

The two equations are:
\( -10x + 10y = 20 \)
\( 9x - 10y = -10 \)

Adding them together: \( (-10x + 9x)+(10y - 10y)=20+( - 10) \)
Simplify: \( -x=10 \)

Step2: Solve for \( x \)

Multiply both sides by -1: \( x = - 10 \)

Step3: Substitute \( x=-10 \) into one of the original equations to find \( y \)

Let's use the first equation \( -10x + 10y = 20 \)

Substitute \( x = - 10 \): \( -10\times(-10)+10y = 20 \)
Simplify: \( 100 + 10y = 20 \)

Subtract 100 from both sides: \( 10y=20 - 100 \)
\( 10y=-80 \)

Divide both sides by 10: \( y=-8 \)

Answer:

\((-10, -8)\)