Question

add the equations to eliminate the y-terms. \\(4x - 8y = 20\\) \\(3x + 4y = 5\\) \\(\times 2\\) \\(\downarrow\\) \\(\downarrow\\) \\(4x - 8y = 20\\) \\(6x + 8y = 10\\) \\(+\\) \\(\boxed{?}\\) \\(=\\) \\(\boxed{?}\\)

Explanation:

Step1: Add the x - terms

We have the equations \(4x - 8y = 20\) and \(6x+8y = 10\). When adding the x - terms, we add the coefficients of \(x\) together. So \(4x+6x=(4 + 6)x=10x\).

Step2: Add the y - terms

For the y - terms, we have \(-8y+8y\). Since the coefficients of \(y\) are \(- 8\) and \(8\), their sum is \((-8 + 8)y = 0y\), which means the \(y\) - terms are eliminated.

Step3: Add the constant terms

For the constant terms, we add \(20\) and \(10\). So \(20 + 10=30\).

Step4: Combine the results

Putting it all together, we get \(10x+0y = 30\), or simply \(10x=30\).

Answer:

\(10x = 30\)