Question

use the elimination method to solve the system of equations. choose the correct ordered pair.

$7x + 4y = 39$
$2x + 4y = 14$

a. $(5, 1)$
b. $(3, 4)$
c. $(3, 2)$
d. $(5, 4)$

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}7x + 4y = 39\\2x + 4y = 14\end{cases}$$

Subtract the second equation from the first to eliminate \(y\):
$$(7x + 4y)-(2x + 4y)=39 - 14$$
Simplify the left - hand side: \(7x+4y - 2x - 4y=5x\), and the right - hand side: \(39 - 14 = 25\). So we get \(5x=25\).

Step2: Solve for \(x\)

Divide both sides of the equation \(5x = 25\) by 5:
\(x=\frac{25}{5}=5\)

Step3: Substitute \(x = 5\) into one of the original equations

Substitute \(x = 5\) into the second equation \(2x+4y = 14\):
\(2\times5+4y=14\)
Simplify the left - hand side: \(10 + 4y=14\)
Subtract 10 from both sides: \(4y=14 - 10=4\)
Divide both sides by 4: \(y = 1\)

Answer:

A. \((5,1)\)