Question

Use the substitution method to solve the linear system. $$\begin{aligned} &x-y=-5\\\ &x+4=16 \end{aligned}$$

Short answer

The solution to the linear system is \(x = 12, y = 17\).

Step-by-step solution

Solve Second Equation

Solving the second equation \(x + 4 = 16\) for \(x\), it can be seen that subtracting 4 from both sides gives \(x = 16 - 4 = 12\)

Substitute Value into First Equation

Now substitute the value of \(x = 12\) into the first equation \(-y = 12-x = -5\). This gives \(y = 12 - (-5) = 17\).

Result

The solution to the linear system using the substitution method is \(x = 12, y = 17\).