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

Answer:

See Explanation

Step-by-step 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

$x = -6/-2$

$x = 3$