# Solve the following system of equations using elimination: x + y = 6 -x + 7y = 2

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We have to solve the following system of equations using elimination:

x + y = 6 ...(1)

-x + 7y = 2 ...(2)

First let's eliminate x

Add (1) and (2)

=> 8y = 8

=> y = 1

Now let's eliminate y

7*(1) - (2)

=> 7x + 7y + x - 7y = 42 - 2

=> 8x = 40

=> x = 5

**The solution of the system of equations is x = 5 and y = 1**

*Using elimination method:*

Equations are : x+y=6 ..... *(1)*

-x+7y=2 .....*(2)*

Adding equation *(1)* & *(2)* we get ...

x+ y=6

+ -x+7y=2

___________

8y=8

As we can see, the x and -x cancelled out, therefore eliminating the variable x, leaving an equation with only one variable (y), able to be solved.

8y=8

=> y=1

Now that we have a value for y, we must find one for x. To do this, just substitute the value for y into either original equation, and solve it for x

So, now putting the value for y (y=1) into equation *(1)*

x + 1=6

=> x=6-1

=> x=5

Solution for these two equations is *x=5 & y=1.*