Question

solve using elimination.
x - 6y = -20
-x + 4y = 10
(\square, \square)
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Explanation:

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

The first equation is \(x - 6y=-20\) and the second is \(-x + 4y = 10\). Adding them together: \((x - 6y)+(-x + 4y)=-20 + 10\). Simplifying the left side: \(x - x-6y + 4y=-2y\), and the right side: \(-10\). So we have \(-2y=-10\).

Step2: Solve for \(y\)

Divide both sides of \(-2y=-10\) by \(-2\): \(y=\frac{-10}{-2}=5\).

Step3: Substitute \(y = 5\) into one of the original equations to find \(x\)

Let's use the first equation \(x-6y=-20\). Substitute \(y = 5\): \(x-6\times5=-20\), which simplifies to \(x - 30=-20\). Add 30 to both sides: \(x=-20 + 30 = 10\).

Answer:

\((10,5)\)