Question

svlc algebra 1a - standard (15260)
solving systems: introduction to linear combinations
what is the solution to this system of linear equations?
$2x + y = 1$
$3x - y = -6$
$(2, 3)$ $(-1, 3)$
$(5, 0)$ $(1, -1)$

Explanation:

Step1: Add the two equations

We have the system:
\[

$$\begin{cases} 2x + y = 1 \\ 3x - y = -6 \end{cases}$$

\]
Adding the two equations together: \((2x + y)+(3x - y)=1+(-6)\)
Simplify the left side: \(2x + y+3x - y = 5x\)
Simplify the right side: \(1 - 6=-5\)
So we get \(5x=-5\)

Step2: Solve for x

Divide both sides of \(5x = - 5\) by 5: \(x=\frac{-5}{5}=-1\)

Step3: Substitute x into one equation

Substitute \(x = - 1\) into the first equation \(2x + y=1\):
\(2\times(-1)+y = 1\)
Simplify: \(-2 + y=1\)
Add 2 to both sides: \(y=1 + 2=3\)

Answer:

\((-1,3)\)