Question

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

Answer 1

`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`

Answer 2

`(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)`

Answer 3

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)`