Question

Graph the system of equations on graph paper.

[Picture will have the equation here]

Which statements are true about the solution to the system of equations?

Select each correct answer.


A) The ordered pair that is the solution to the system lies in Quadrant I .

B) The y-coordinate of the solution is 3.

C) The ordered pair that is the solution to the system lies in Quadrant IV .

D) The x-coordinate of the solution is 2.

E) The y-coordinate of the solution is −2 .

F) The x-coordinate of the solution is 3.

Answer 1

6x + 4y = 24
2x - 4y = -8

We will use the addition method in solving this system of equation.

6x + 4y = 24
+ (2x - 4y = -8)
8x + 0 = 16

8x = 16
x = 16/8
x = 2

Let us substitute x by its value to get the value of y.

6x + 4y = 24
→ 6(2) + 4y = 24
12 + 4y = 24
4y = 24 - 12
4y = 12
y = 12/4
y = 3

2x - 4y = - 8
→ 2(2) - 4y = - 8
4 - 4y = - 8
-4y = - 8 - 4
-4y = -12
y = -12/-4
y = 3

So x = 2 and y = 3. → (2,3)

The true statement among the choices are:

A) The ordered pair that is the solution to the system lies in Quadrant I .
B) The y-coordinate of the solution is 3.
D) The x-coordinate of the solution is 2.