Question

Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A. A. x + 3y = 11 → x + 3y = 11 5x − y = 17 → 15x − 3y = 51 15x = 62 B. x + 3y = 11 15x = 62 What is the solution to both systems A and B?

Answer 1

we have that

System A

`x+3y=11`

System B

`5x-y=17`

Step
`1`

Multiply System B by
`3`

`3*(5x-y)=3*17`

`15x-3y=51`

Step
`2`

Find the sum system A and system B

`x+3y=11`

`15x-3y=51\\ ------`

`16x=62`

`x=(62)/(16) \\ \\ x=(31)/(8)`

`x=3.875`

Find the value of y

`5x-y=17`

`5x-y=17\\ y=5*(31)/(8) -17\\ \\ y=((155-8*17))/(8) \\ \\ y=(19)/(8) \\ \\ y=2.375`

therefore

the answer is

the solution of the system is the point
`(3.875,2.375)`

see the attached figure