Question

solve the system using the elimination method. write the solution
3x + 2y = 22
x + 4y = 2
( , )

Explanation:

Step1: Write given system

$$\begin{cases} 3x + 2y = 22 \\ -x + 4y = 2 \end{cases}$$

Step2: Eliminate $x$, multiply eq2 by 3

$$-3x + 12y = 6$$

Step3: Add to eq1, solve for $y$

$$(3x + 2y) + (-3x + 12y) = 22 + 6$$
$$14y = 28$$
$$y = \frac{28}{14} = 2$$

Step4: Substitute $y=2$ into eq2

$$-x + 4(2) = 2$$
$$-x + 8 = 2$$

Step5: Solve equation for $x$

$$-x = 2 - 8 = -6$$
$$x = 6$$

Answer:

$(6, 2)$