Question

What is the solution to this system of linear equations?

2a – 3c = –6

a + 2c = 11

(a) -76/7, 17/7
(b) 3,-4
(c) 3/4
(d) 87/7, -5/7

Answer 1

option c is correct.

3, 4

Explanation:

Given the system of equations:

`2a-3c = -6` .....[1]

`a+2c = 11` .....[2]

Multiply equation [2] by 2 both sides we have;

`2a + 4c= 22` ......[3]

Subtract equation [2] from [3] we have;

`2a+4c - 2a+3c = 22 - (-6)`

⇒
`4c+3c = 28`

Combine like terms;

`7c = 28`

Divide both sides by 7 we have;

c = 4

Substitute this in [1] we have;

2a- 3(4) = -6

2a -12 = -6

Add 12 to both sides we have;

2a = 6

Divide both sides by 3 we have;

a = 3

Therefore, the solution to this system of linear equations is, (3, 4)

Answer 2

option C

`(3,4)`

Explanation:

we have

`2a-3c=-6` -----> equation A

`a+2c=11` -----> equation B

Multiply the equation B by
`-2`

`-2(a+2c)=-2*11`

`-2a-4c=-22` ------> equation C

Adds equation A and equation C

`2a-3c=-6\\-2a-4c=-22\\----------\\-3c-4c=-6-22\\-7c=-28\\c=4`

Find the value of a

substitute the value of c in equation A

`2a-3(4)=-6`

`2a=6`

`a=3`

The solution is the point
`(3,4)`