Question

svlc algebra 1a - standard (15260) solving systems: introduction to linear combinations what is the solution to this system of linear equations? $x - 3y = -2$ $x + 3y = 16$ $(-3, -2)$ $(-2, -3)$ $(7, 3)$ $(3, 7)$

Explanation:

Step1: Add the two equations

The system is:
\[

$$\begin{cases} x - 3y = -2 \\ x + 3y = 16 \end{cases}$$

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

Step2: Solve for x

Divide both sides of the equation \(2x = 14\) by 2: \(x=\frac{14}{2}=7\).

Step3: Substitute x into one of the original equations

Substitute \(x = 7\) into the equation \(x+3y=16\). We get \(7 + 3y=16\).

Step4: Solve for y

Subtract 7 from both sides of the equation \(7+3y = 16\): \(3y=16 - 7=9\).
Then divide both sides by 3: \(y=\frac{9}{3}=3\).

Answer:

\((7,3)\)