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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)

User Zzzirk
by
8.9k points

2 Answers

3 votes

Answer:

Its C.

{8, 14/3}

User Last
by
8.5k points
3 votes

Answer:


(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))

User Satyen Udeshi
by
7.2k points

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