Question

Two linear equations are shown. A coordinate grid with 2 lines. The first line is labeled y equals StartFraction one-third EndFraction x plus 2 and passes through (negative 6, 0) and (0, 2). The second line is labeled y equals StartFraction 4 over 3 EndFraction minus 5. What is the solution to the system of equations? (7, 4) (7, StartFraction 13 over 3 EndFraction) (8, StartFraction 14 over 3 EndFraction) (9, 7)

Answer 1

Its C.

{8, 14/3}

Answer 2

`(7,(13)/(3))`

Explanation:

we have

The equation of the first line

`y=(1)/(3)x+2` ------> equation A

The equation of the second line

`y=(4)/(3)x-5` ------> equation B

Solve the system of equations by elimination

Multiply equation A by -4 both sides

`(-4)y=(-4)((1)/(3)x+2)`

`-4y=-(4)/(3)x-8` --------> equation C

Adds equation B and equation C

`y=(4)/(3)x-5\\-4y=-(4)/(3)x-8\\--------\\y-4y=-5-8\\-3y=-13\\y=(13)/(3)`

Find the value of x

substitute the value of y

`(13)/(3)=(1)/(3)x+2`

`(1)/(3)x=(13)/(3)-2`

Multiply by 3 both sides

`x=13-6`

`x=7`

therefore

The solution to the system of equations is the point
`(7,(13)/(3))`