Question

Use substitution to solve the linear system. $$\begin{aligned} &x-y=0\\\ &x+y=2 \end{aligned}$$

Short answer

The solution to this system of equations is \(x = 1\) and \(y = 1\).

Step-by-step solution

Express one variable in terms of the other from the first equation

From the first equation, \(x - y = 0\), we rearrange it to express \(x\) in terms of \(y\). This gives us \(x = y\).

Substitute the value of x into the second equation

Next, substitute \(x = y\) from the first equation into the second equation. This gives us, \(y + y = 2\), which simplifies to \(2y = 2\).

Solve for y

We solve the previous equation for \(y\), which gives us \(y = 2/2 = 1\).

Substitute y value into one of the equations to find x

Then, we substitute \(y = 1\) into the first equation \(x – y = 0\) to find \(x\). This results in \(x = 1+0 = 1\).