Solve the following system of equations using elimination: x + y = 6 -x + 7y = 2
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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.