Question

what is the value of y in the following system of equations?
2x + 3y = 6
2x + y = -2
2
1
-3
4
16 multiple choice 2 points
which ordered pair is the solution of the following system of equations?
3x + 2y = 4
-2x + 2y = 24
(-4, 8)
(2, -5)
(2, -1)
(-4, -8)
17 multiple choice 2 points
what is the solution for the following system of equations?
2x + y = 7
x - 2y = 6
(-1, 4)
(1, 3)
(3, 1)
(4, -1)

Explanation:

Problem 1:

Step1: Subtract the two equations

$(2x + 3y) - (2x + y) = 6 - (-2)$
$2y = 8$

Step2: Solve for y

$y = \frac{8}{2} = 4$

Problem 2:

Step1: Subtract the two equations

$(3x + 2y) - (-2x + 2y) = 4 - 24$
$5x = -20$

Step2: Solve for x

$x = \frac{-20}{5} = -4$

Step3: Substitute x into first equation

$3(-4) + 2y = 4$
$-12 + 2y = 4$
$2y = 16$
$y = 8$

Problem 3:

Step1: Isolate y from first equation

$y = 7 - 2x$

Step2: Substitute y into second equation

$x - 2(7 - 2x) = 6$
$x - 14 + 4x = 6$
$5x = 20$

Step3: Solve for x

$x = \frac{20}{5} = 4$

Step4: Solve for y

$y = 7 - 2(4) = 7 - 8 = -1$

Answer:

1. 4
2. (-4, 8)
3. (4, -1)