Question

1. solve for x and y. x + y = 7 and x - y = 1. type a response

Explanation:

Step1: Add the two equations

We have the system of equations:

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Adding the two equations together: \((x + y)+(x - y)=7 + 1\).
Simplifying the left - hand side: \(x + y+x - y = 2x\), and the right - hand side is \(8\). So we get \(2x=8\).

Step2: Solve for x

Divide both sides of the equation \(2x = 8\) by \(2\): \(x=\frac{8}{2}=4\).

Step3: Substitute x into one of the original equations to solve for y

Substitute \(x = 4\) into the equation \(x + y=7\). We get \(4 + y=7\).
Subtract \(4\) from both sides: \(y=7 - 4 = 3\).

Answer:

\(x = 4\), \(y = 3\)