Question

Two systems of equations are shown. 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.

Answer 1

(4,3)

Explanation:

I took the test.

Answer 2

`x = 3.875`

`y = 2.375`

Explanation:

See comment for complete question.

Given

A.

`x + 3y = 11 => x + 3y = 11`

`5x - y = 17 => 15x - 3y = 51`

`16x = 62`

B.

`x + 3y = 11`

`16x = 62`

Required

Determine the values of x and y

The first equation in B is:

`x + 3y = 11`

In (a): 5x - y = 17 is multiplied by 3, then added to x + 3y = 11.

So, the second equation is:

`5x - y = 17`

Solving (a) & (b):

`x + 3y = 11` --- (1)

`5x - y = 17` ---- (2)

Make x the subject in (1)

`x + 3y = 11`

`x = 11 - 3y`

Substitute
`11 - 3y` for x in
`5x - y = 17`

`5(11 - 3y) - y = 17`

Open bracket

`55 - 15y - y = 17`

`55 - 16y = 17`

Collect Like Terms

`- 16y = 17-55`

`- 16y = -38`

Solve for y

`y = (-38)/(-16)`

`y = (38)/(16)`

`y = 2.375`

Substitute 2.375 for y in
`x = 11 - 3y`

`x = 11 - 3 * 2.375`

`x = 11 - 7.125`

`x = 3.875`