How do you solve the system of equations 9x + y = 8 and - 7x - 2y = 6?

3 Answers
Jan 27, 2018

x=2
y=-10

Explanation:

9x+y=8 ...(1)
-7x-2y=6 ...(2)

multiply for 2 the equation (1)

(2)(9x+y=8)
-7x-2y=6

18x+2y=16
-7x-2y=6

now adding both equations

18x-7x+2y-2y=16+6

11x=22
x=2

for y just replace in any equation

in (1)

9(2)+y=8
18+y=8
y=8-18

y=-10

Jan 27, 2018

(x,y)to(2,-10)

Explanation:

9x+y=8to(1)

-7x-2y=6to(2)

"from equation "(1)

y=8-9xto(3)

"substitute "y=8-9x" in equation "(2)

-7x-2(8-9x)=6

rArr-7x-16+18x=6

rArr11x-16=6

"add 16 to both sides"

rArr11x=22

"divide both sides by 11"

rArrx=2

"substitute "x=2" in equation "(3)

rArry=8-18=-10

"point of intersection "=(2,-10)

Jan 27, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for y:

9x + y = 8

9x - color(red)(9x) + y = 8 - color(red)(9x)

0 + y = 8 - 9x

y = 8 - 9x

Step 2) Substitute (8 - 9x) for y in the second equation and solve for x:

-7x - 2y = 6 becomes:

-7x - 2(8 - 9x) = 6

-7x - (2 xx 8) + (2 xx 9x) = 6

-7x - 16 + 18x = 6

-7x + 18x - 16 = 6

(-7 + 18)x - 16 = 6

11x - 16 = 6

11x - 16 + color(red)(16) = 6 + color(red)(16)

11x - 0 = 22

11x = 22

(11x)/color(red)(11) = 22/color(red)(11)

(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 2

x = 2

Step 3) Substitute 2 for x in the solution to the first equation at the end of Step 1 and calculate y:

y = 8 - 9x becomes:

y = 8 - (9 xx 2)

y = 8 - 18

y = -10

The Solution Is:

x = 2 and y = -10

Or

(2, -10)