Question

solve.
-3x + 2y = -6
-6x + 6y = 6
(□, □)
submit

Explanation:

Step1: Simplify the equations

We have the system of equations:

1. \(-3x + 2y = -6\)
2. \(-6x + 6y = 6\)

Let's multiply the first equation by 2 to make the coefficients of \(x\) in both equations have a common multiple.
\(2\times(-3x + 2y)=2\times(-6)\)
\(-6x + 4y = -12\)

Step2: Subtract the equations

Now we have two equations:

• \(-6x + 4y = -12\) (from the first equation after multiplication)
• \(-6x + 6y = 6\) (the second original equation)

Subtract the first new equation from the second equation:
\((-6x + 6y)-(-6x + 4y)=6 - (-12)\)
Simplify the left side: \(-6x + 6y + 6x - 4y = 2y\)
Simplify the right side: \(6 + 12 = 18\)
So we get \(2y = 18\), then divide both sides by 2: \(y=\frac{18}{2}=9\)

Step3: Substitute y into the first equation

Substitute \(y = 9\) into the first original equation \(-3x + 2y=-6\):
\(-3x + 2\times9=-6\)
\(-3x + 18=-6\)
Subtract 18 from both sides: \(-3x=-6 - 18=-24\)
Divide both sides by -3: \(x=\frac{-24}{-3}=8\)

Answer:

\((8, 9)\)