# Solve using the elimination method: x+y=4 x-y=-2

## Question:

Solve using the elimination method:

{eq}x+y=4 \\ x-y=-2 {/eq}

## System of Linear Equations; Elimination Method:

{eq}\\ {/eq}

The method of elimination is a useful tool that will be used here in order to get the solution or a pair of values of {eq}x {/eq} and {eq}y {/eq} such that both the equations satisfy simultaneously. In this method, we just have to eliminate any one of the variables using basic mathematical operations. To eliminate the variable, just make the coefficient of that variable equal and opposite in value in both the equations, and then just add them.

{eq}\\ {/eq}

{eq}x + y = 4 \; \; \cdots \cdots \; \; (1) \\ x - y = -2 \; \; \cdots \cdots \; \; (2) {/eq}

Now add equation (1) and equation (2) in order to eliminate the variable {eq}y {/eq}:

{eq}(x + y- 4) + (x - y + 2) = 0 \\ 2x - 2 = 0 \\ \Longrightarrow x = 1 {/eq}

Now put the value of {eq}x = 1 {/eq} in equation (1) in order to get the value of {eq}y {/eq}:

{eq}1 + y = 4 \\ \Longrightarrow y = 3 {/eq}

Finally, we have the values of {eq}x {/eq} and {eq}y {/eq}:

{eq}\Longrightarrow \boxed {(x, \; y) = (1, \; 3)} {/eq}