Question

1. solve: 2x + 3y = 14, 2x - 3y = 2. type a response

Explanation:

Step1: Add the two equations

We have the system of equations:

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Adding the two equations to eliminate \(y\):
\((2x + 3y)+(2x - 3y)=14 + 2\)
Simplify the left - hand side: \(2x+3y + 2x-3y=4x\), and the right - hand side: \(14 + 2 = 16\). So we get \(4x=16\).

Step2: Solve for \(x\)

Divide both sides of the equation \(4x = 16\) by 4: \(x=\frac{16}{4}=4\).

Step3: Substitute \(x = 4\) into one of the original equations

Substitute \(x = 4\) into the first equation \(2x+3y = 14\). We have \(2\times4+3y=14\), which simplifies to \(8 + 3y=14\).

Step4: Solve for \(y\)

Subtract 8 from both sides of the equation \(8 + 3y=14\): \(3y=14 - 8=6\). Then divide both sides by 3: \(y=\frac{6}{3}=2\).

Answer:

The solution to the system of equations is \(x = 4\) and \(y=2\), or the ordered pair \((4,2)\).