Question

Solve the system of equations using the linear combination method.
7x+2y=29
3x-5y=30

Answer 1

Explanation:

Answer 2

For this case we have a system of two linear equations with two unknowns. whose variables are given by x and y respectively.

To solve the system by the linear combination method we follow the following steps:

1st step:

We multiply the first equation by 5:

`35x + 10y = 145`

2nd step:

We multiply the second equation by 2:

`6x-10y = 60`

3rd step:

We add the equations:

`35x + 10y = 145\\6x-10y = 60`

Thus, we obtain the following:

`41x = 205`

`x =(205)/(41)`

`x = 5`

4th step:

We substitute
`x= 5` in any of the equations:

`3 (5) -5y = 30\\15-5y = 30\\-5y = 30-15\\-5y = 15`

`y =(15)/(-5)\\y = -3`

Thus, the values of the variables are
`x = 5`and
`y = -3`.

Answer:

The values are:
`x = 5`and
`y = -3`.