Solve the system of equations : 2x-y=-2 ; x+3y=13 by elimination method.

We are asked to solve the system of equations, 2x-y = -2;
x+3y =13, by the elimination method.

We will begin by
multiplying the first equation by 3.  This will result in the coefficients of the y in
both equations being additive inverses.

3[2x - y = -2]
=> 6x -3y = -6

We will now combine the 2
equations.

=> 6x - 3y =
-6

x + 3y = 13

=> 7x =
7

=>  x = 1

Substitute
the x value of 1 into the given equation x + 3y =13 to solve for
y.

=> x + 3y =
13

=> 1 + 3y =
13

=>  3y =
12

=>   y =
4

The solution set of the system is (1,
4).