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

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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).**

We have to solve the system of equations:

2x - y = -2 ...(1)

x + 3y = 13 ...(2)

1 - 2*(2)

=> 2x - y - 2x - 6y = -2 - 26

=> -7y = -28

=> y = -28/-7

=> y = 4

3*(1) + (2)

=> 6x - 3y + x + 3y = -6 + 13

=> 7x = 7

=> x = 1

**The solution of the equation is x = 1 and y = 4**