# Solve the system of equation by using the elimination method: x+6y=12 -x+7y=1

## Question:

Solve the system of equation by using the elimination method:

{eq}\ \ \ x+6y=12 \\ -x+7y=1 {/eq}

## Elimination Method:

{eq}\\ {/eq}

The method of elimination is a powerful tool in order to get the solution of two equations in terms of two variables. In this method, we just have to replace one variable in terms of another variable into other equation than just perform some basic mathematical operation to get the value of the substituted variable. Then substituted back the value in any of the equations in order to get the value of eliminated variable.

{eq}\\ {/eq}

The set of equations for which we have to determine the solution is given as:

{eq}x + 6y = 12 \; \; \cdots \cdots \; \; (1) \\ -x + 7y = 1 \; \; \cdots \cdots \; \; (2) {/eq}

Now add the equation (1) and (2) in order to eliminate the variable {eq}\; x \; {/eq} and get an equation only in terms of variable {eq}\; y \; {/eq}:

{eq}(x + 6y - 12) + (-x + 7y - 1) = 0 {/eq}

{eq}6y + 7y = 13 \; \; \; \Longrightarrow \; \; y = 1 {/eq}

Now substitute the value of {eq}\; y = 1 \; {/eq} in equation (1):

{eq}x + 6 \times 1 = 12 \; \; \; \Longrightarrow \; \; x = 6 {/eq}

Finally, we have the solution to the given equations:

{eq}\Longrightarrow \boxed {(x, \; y) = (6, \; 1)} {/eq}