Question

1) y = 6x − 11 −2x − 3y = −7 4) −3x − 3y = 3 y = −5x − 17 7)−4x + y = 6 −5x − y = 21 8) −7x − 2y = −13 x − 2y = 11 18) −2x + 6y = 6 −7x + 8y = −5 My teacher started a new unit and i wasn't hear to get the teaching so i chose some random problems and hopefully one of them is easy enough for you to teach me how to do it

Answer 1

See Explanation

Explanation:

1.

Given

`y = 6x - 11`

`-2x - 3y = -7`

Solve for x and y

In the first equation, we have:
`y = 6x - 11`

Substitute
`6x - 11` for
`y` in the second

`-2x - 3y = -7`

`-2x - 3(6x - 11) = -7`

`-2x - 18x + 33 = -7`

`-20x+ 33 = -7`

`-20x= -7-33`

`-20x= -40`

Divide through by -1

`20x = 40`

`x = 40/20`

`x = 2`

Recall that:

`y = 6x - 11`

`y = 6 * 2 - 11`

`y = 1`

2,

Given

`-3x - 3y = 3`

`y = -5x - 17`

In the second equation, we have:
`y = -5x - 17`

Substitute
`-5x - 17` for
`y` in the first equation

`-3x - 3y = 3`

`-3x - 3(-5x - 17) = 3`

`-3x + 15x + 51 = 3`

`12x + 51 = 3`

`12x=3 - 51`

`12x=-48`

`x = -48/12`

`x = -4`

Recall that:
`y = -5x - 17`

`y = -5 * -4 - 17`

`y = -3`

3. Given

`-4x + y = 6`

`-5x - y = 21`

Add both equations to eliminate y

`-4x - 5x + y - y = 6 + 21`

`-9x= 27`

Solve for x

`x = 27/-9`

`x = -3`

Substitute -3 for x in the first equation:
`-4x + y = 6`

`-4 * -3 + y = 6`

`12 + y = 6`

`y = 6 - 12`

`y = -6`

4. Given

`-7x - 2y = -13`

`x - 2y = 11`

Make x the subject in the second equation

`x - 2y = 11`

`x = 11 + 2y`

Substitute 11 + 2y for x in the first equation

`-7x - 2y = -13`

`-7 (11 + 2y) - 2y = -13`

`-77 -14y - 2y = -13`

`-77 -16y = -13`

`-16y = -13 + 77`

`-16y = 64`

`y = 64/-16`

`y = -4`

Substitute -4 for y in
`x = 11 + 2y`

`x = 11 + 2 * -4`

`x = 11 -8`

`x = 3`

5. Given

`-2x + 6y = 6`

`-7x + 8y = -5`

Multiply the first equation by 7 and the second by - 2 to eliminate x

The first

`7(-2x + 6y = 6)`

`-14x + 42y =42`

The second

`-2(-7x + 8y = -5)`

`14x - 16y = 10`

Add the resulting equations

`-14x + 42y =42`

`14x - 16y = 10`

------------------------------

`-14x + 14x + 42y - 16y = 42 + 10`

`42y - 16y = 42 + 10`

`26y = 52`

Solve for y

`y = 52/26`

`y = 2`

Substitute 2 for y in
`-2x + 6y = 6`

`-2x + 6 * 2 = 6`

`-2x + 12 = 6`

`-2x = 6 -12`

`-2x = -6`

Solve for x

`x = -6/-2`

`x = 3`