Question

solve using elimination.
3x - 4y = 13
-4x + 8y = -20
(□, □)

Explanation:

Step1: Simplify the second equation

Divide the second equation \(-4x + 8y = -20\) by \(-4\) to simplify. We get \(x - 2y = 5\), which can be rewritten as \(x = 2y + 5\). But we can also use elimination directly. Let's multiply the first equation \(3x - 4y = 13\) by \(2\) to make the coefficients of \(y\) opposite. So \(2\times(3x - 4y)=2\times13\), which gives \(6x - 8y = 26\).

Step2: Add the two equations

Now add the new first equation \(6x - 8y = 26\) and the second original equation \(-4x + 8y = -20\). \((6x - 8y)+(-4x + 8y)=26+(-20)\). The \(-8y\) and \(+8y\) cancel out, so \(6x - 4x=6\), which simplifies to \(2x = 6\).

Step3: Solve for x

Divide both sides of \(2x = 6\) by \(2\). So \(x=\frac{6}{2}=3\).

Step4: Substitute x into one of the original equations

Substitute \(x = 3\) into the first original equation \(3x - 4y = 13\). We get \(3\times3 - 4y = 13\), which is \(9 - 4y = 13\).

Step5: Solve for y

Subtract \(9\) from both sides: \(-4y = 13 - 9 = 4\). Then divide both sides by \(-4\): \(y=\frac{4}{-4}=-1\). Wait, but the problem shows a box with "I" for y? Maybe a typo, but following the calculation, y is -1? Wait, let's check again. Wait, when we substitute x = 3 into \(3x - 4y = 13\): \(9 - 4y = 13\), so \(-4y = 4\), so \(y = -1\). But the problem's second box has "I", maybe a typo. But according to the elimination steps, x is 3.

Answer:

\((3, -1)\) (assuming the "I" is a typo and the correct y is -1)