How do you solve the system of equations x= 6y - 7 and x + 6y = 9?

2 Answers
smendyka
Jan 26, 2018

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for x we can substitute (6y - 7) for x in the second equation and solve for y:

x + 6y = 9 becomes:

(6y - 7) + 6y = 9

6y - 7 + 6y = 9

6y + 6y - 7 = 9

(6 + 6)y - 7 = 9

12y - 7 = 9

12y - 7 + color(red)(7) = 9 + color(red)(7)

12y - 0 = 16

12y = 16

(12y)/color(red)(12) = 16/color(red)(12)

y = 4/3

Step 2) Substitute 4/3 for y in the first equation and calculate x:

x = 6y - 7 becomes

x = (6 xx 4/3) - 7

x = 24/3 - 7

x = 8 - 7

x = 1

The Solution Is:

x = 1 and y = 4/3

Or

(1, 4/3)

Irene
Jan 26, 2018

X=1, y= 8/6

Explanation:

Rearrange equations to be in the form of x=...
Ie.
x=9-6y

Make these equations equal to each other
6y-7=9-6y

16=12y

y=16/12 =8/6

Find x
x=9-6(8/6) =9-8= 1

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