Question

I need help with this queston

Use the linear combination method to solve this system of equations. What is the value of x?

Answer 1

(55/27, 32/9)

Explanation:

The system of equations is

`3x+7y=31 \\3x-2y=-1`

The first step is to arrange like terms in colums, which is already done.

Then, we need to multiply a number by one equation in such way where we get opposite like terms. Notice that we need to multiply the first equation by -1

`-3x-7y=-31\\3x-2y=-1`

Then, we sum equations to obtain the value of one variable.

`0-9y=-32\\y=(-32)/(-9)\\ y=(32)/(9)`

Now, we use this value to find the second variable

`3x-2y=-1\\3x-2((32)/(9) )=-1\\3x=-1+(64)/(9)\\ 3x=(-9+64)/(9)\\ 3x=(55)/(9)\\ x=(55)/(27)`

Therefore, the solution is (55/27, 32/9).

(The image attached shows the graphic solution)