Solve the systems of linear equations be elimination:

Question

How do I solve this? Please don't just put an answer alone, can you explain so I can understand?

y = x - 4

x + y = 6

Answer 1

First, you will rewrite these so that the x's and y's are underneath each other like this

-x + y = -4

x + y = 6

Next add the two equations, so that one of the variables cancels out.

-x +x + y + y = 2 which leads to

2y = 2 solve for y to get y = 1

Put the y result into either of the original equations and solve for x like this

x + 1 = 6 or x = 5. Prove by putting both x and y values into either original equation which should add up to the constant term.

Note: this is a simple example. In other cases you will have to multiply by some number so that the equations can be added so one variable will cancel.

Answer 2

Or, solve the 2nd for y.

y = x - 4

y = 6 - x

x - 4 = 6 - x

2x = 10

x = 5

y = 6 - 5

y = 1

(5,1)

Answer 3

-x + y = -4

x + y = 6

2y = 2

y=1 ---> x=5

the solution is (5,1)