Question

1. \

$$\begin{cases} 2x + 5y = 14 \\\\ 4x + 2y = -4 \\end{cases}$$

Explanation:

Step1: Eliminate x by multiplying first equation

Multiply the first equation \(2x + 5y = 14\) by 2: \(4x + 10y = 28\)

Step2: Subtract second equation from new equation

Subtract \(4x + 2y = -4\) from \(4x + 10y = 28\):
\((4x - 4x)+(10y - 2y)=28 - (-4)\)
\(8y = 32\)

Step3: Solve for y

Divide both sides by 8: \(y=\frac{32}{8}=4\)

Step4: Substitute y into first equation

Substitute \(y = 4\) into \(2x + 5y = 14\):
\(2x + 5(4)=14\)
\(2x + 20 = 14\)

Step5: Solve for x

Subtract 20: \(2x=14 - 20=-6\)
Divide by 2: \(x=\frac{-6}{2}=-3\)

Answer:

\(x = -3\), \(y = 4\)