Question

solve using elimination.
-4x - 6y = -10
x - 3y = 16
(\boxed{\space}, \boxed{\space})

Explanation:

Step1: Multiply the second equation by 2

To eliminate \(y\), we multiply the second equation \(x - 3y = 16\) by 2. This gives us \(2x - 6y = 32\).

Step2: Subtract the first equation from the new equation

Now we have the first equation \(-4x - 6y = -10\) and the new equation \(2x - 6y = 32\). Subtract the first from the second: \((2x - 6y) - (-4x - 6y) = 32 - (-10)\). Simplifying, we get \(2x - 6y + 4x + 6y = 32 + 10\), which simplifies to \(6x = 42\).

Step3: Solve for \(x\)

Divide both sides of \(6x = 42\) by 6: \(x=\frac{42}{6}=7\).

Step4: Substitute \(x = 7\) into the second equation

Substitute \(x = 7\) into \(x - 3y = 16\): \(7 - 3y = 16\).

Step5: Solve for \(y\)

Subtract 7 from both sides: \(-3y = 16 - 7 = 9\). Then divide by -3: \(y=\frac{9}{-3}=-3\).

Answer:

\((7, -3)\)