Question

graph the system of equations on graph paper.\

$$\begin{cases}6x + 4y = 24\\\\2x - 4y = -8\\end{cases}$$

\which statements are true about the solution to the system of equations?\select each correct answer.\\ \\(\square\\) the ordered pair that is the solution to the system lies in quadrant i.\\ \\(\square\\) the y-coordinate of the solution is -2.\\ \\(\square\\) the y-coordinate of the solution is 3.\\ \\(\square\\) the x-coordinate of the solution is 2.\\ \\(\square\\) the x-coordinate of the solution is 3.

Explanation:

Step1: Add the two equations

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

Step2: Solve for $x$

$$x = \frac{16}{8} = 2$$

Step3: Substitute $x=2$ into first equation

$$6(2) + 4y = 24$$
$$12 + 4y = 24$$

Step4: Solve for $y$

$$4y = 24 - 12$$
$$4y = 12$$
$$y = \frac{12}{4} = 3$$

Step5: Verify solution quadrant

The solution is $(2, 3)$, which has positive $x$ and $y$ values, so it lies in Quadrant I.

Answer:

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