Question

1. 4x + y = 2

x - y = 3

Explanation:

Step1: Add the two equations

We have the system of equations:

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Adding the two equations together to eliminate \(y\):
\((4x + y)+(x - y)=2 + 3\)
Simplify the left - hand side: \(4x+y+x - y=5x\), and the right - hand side is \(5\). So we get \(5x=5\).

Step2: Solve for \(x\)

From \(5x = 5\), divide both sides by \(5\): \(x=\frac{5}{5}=1\).

Step3: Substitute \(x = 1\) into one of the equations

Substitute \(x = 1\) into the second equation \(x - y=3\). We get \(1-y = 3\).

Step4: Solve for \(y\)

Subtract \(1\) from both sides of \(1-y = 3\): \(-y=3 - 1=2\). Multiply both sides by \(- 1\) to get \(y=-2\).

Answer:

The solution to the system of equations is \(x = 1\) and \(y=-2\), or the ordered pair \((1,-2)\).