Question

1. $x - y = 4$

$4x + y = 1$
graph of two lines intersecting on a coordinate plane

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system of equations:
\[

$$\begin{cases} x - y = 4 \\ 4x + y = 1 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations: \((x - y)+(4x + y)=4 + 1\)
Simplify the left - hand side: \(x - y+4x + y=5x\), and the right - hand side is \(5\). So we get the equation \(5x=5\).

Step2: Solve for \( x \)

Divide both sides of the equation \(5x = 5\) by \(5\): \(x=\frac{5}{5}=1\)

Step3: Substitute \( x = 1 \) into one of the original equations to find \( y \)

Substitute \(x = 1\) into the first equation \(x - y=4\). We get \(1-y = 4\)
Subtract \(1\) from both sides: \(-y=4 - 1=3\)
Multiply both sides by \(- 1\): \(y=-3\)

Answer:

The solution of the system of equations is \(x = 1,y=-3\)