Question

what is the solution to this system of linear equations?
3x - 2y = 14
5x + y = 32
(3, 5)
(6, 2)
(8, -1)
(14, -18)

Explanation:

Step1: Solve the second equation for y

From \(5x + y = 32\), we can express \(y\) as \(y = 32 - 5x\).

Step2: Substitute y into the first equation

Substitute \(y = 32 - 5x\) into \(3x - 2y = 14\):
\[

$$\begin{align*} 3x - 2(32 - 5x)&= 14\\ 3x - 64 + 10x&= 14\\ 13x - 64&= 14\\ 13x&= 14 + 64\\ 13x&= 78\\ x&= \frac{78}{13}\\ x&= 6 \end{align*}$$

\]

Step3: Find y using x = 6

Substitute \(x = 6\) into \(y = 32 - 5x\):
\(y = 32 - 5\times6 = 32 - 30 = 2\)

Answer:

(6, 2)