Question

Question #6a010

Answer 1

Consider the following system.

`{(x + y = 5), (-2x + 5y = 4):}`

Now, the addition/subtraction method is used to eliminate one of the variables. We can do this to the above equation for `x` by multiplying the first equation by `2` and using the addition method.

`1)" "2(x + y) = 2(5)`

`2x + 2y= 10`

The system becomes:

`{(2x + 2y = 10), (-2x + 5y = 4):}`, which can be solved by elimination:

`0x + 7y = 14`

`y = 2`

`x +y = 5`

`x + 2 = 5`

`x = 3`

Practice exercises:

1. Solve each system through elimination.

a) `{(x - 6y = -1), (4x + y = 21):}`

b) `{(3x + 4y = -2), (7x - 3y = 20):}`

Hopefully this helps, and good luck!