Question

solve the following system of equations using elimination:
$x + y = 2$
$x - y = 4$
a $(2,2)$
b $(1,3)$
c $(3,-1)$
d $(4,-2)$

Explanation:

Step1: Add the two equations

We have the system of equations:
\[

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

\]
Adding the two equations together: \((x + y)+(x - y)=2 + 4\)
Simplifying the left - hand side: \(x + y+x - y = 2x\), and the right - hand side is \(6\). So we get \(2x=6\).

Step2: Solve for x

Divide both sides of the equation \(2x = 6\) by \(2\): \(x=\frac{6}{2}=3\)

Step3: Substitute x into one of the equations to find y

Substitute \(x = 3\) into the first equation \(x + y=2\). We get \(3 + y=2\)
Subtract \(3\) from both sides: \(y=2 - 3=-1\)

Answer:

C. (3,-1)