# Solve using the elimination method.-3x+4y=-19.5 -3x+y=-10.5

## Question:

Solve using the elimination method.

{eq}-3x + 4y = -19.5 {/eq}

{eq}-3x + y = -10.5 {/eq}

## System of Linear Equations; Elimination Method:

{eq}\\ {/eq}

Here we have to solve a system of linear equations or two linear equations in terms of {eq}x {/eq} and {eq}y {/eq}, we will use the method of elimination in order to reach to the solution {eq}(x, \; y) {/eq}. In this method, we just have to eliminate any one of the variables such that we will end up with getting a linear equation in one variable only of the form {eq}\Biggr[ ax + b = 0 \; \; \; \Longrightarrow x = - \dfrac {b}{a} \Biggr] {/eq}, that can be easily solved using the basic operations of algebra.

{eq}\\ {/eq}

The system of equation for which we have to determine the solution is given below:

{eq}-3x + 4y = -19.5 \; \; \; \cdots \cdots \; \; \; (1) \\ -3x + y = -10.5 \; \; \; \cdots \cdots \; \; \; (2) {/eq}

Now perform the operation {eq}(1) - (2) {/eq} in order to eliminate the variable {eq}x {/eq}:

{eq}(-3x + 4y) - (-3x + y) = -19.5 - (-10.5) \\ -3x + 4y + 3x -y = -19.5 + 10.5 \\ 3y = - 9 \\ \Longrightarrow y = - \dfrac {9}{3} = 3 {/eq}

Now put the value of {eq}y = -3 {/eq} in equation (1) in order to get the value of {eq}x {/eq}:

{eq}-3x - 4 \times 3 = -19.5 \\ -3x = -19.5 + 12 \\ -3x = -7.5 \\ \Longrightarrow x = \dfrac {7.5}{3} = 2.5 {/eq}

Finally, we have the solution for the system that is given below:

{eq}\Longrightarrow \boxed {(x, \; y) = (2.5, \; -3)} {/eq}