Question

dominique needs to solve the system of equations by graphing. which statement is true about the system?

(2x - 3y = 12)
(y = -\frac{3}{5}x + 2)

• both equations are in slope-intercept form.
• neither equation is in slope-intercept form.
• the first equation is (y = \frac{2}{3}x - 4) when written in slope-intercept form.
• the second equation is (3x + 5y = 10) when written in slope-intercept form.

Explanation:

Identify the forms of the given equations

Using the Slope-Intercept Form knowledge point
The system of equations is:

$$
LATEXBLOCK0
$$

Convert the first equation to slope-intercept form

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given multiple-choice statements

Using the Graphing Systems knowledge point

• "Both equations are in slope-intercept form" is false.
• "Neither equation is in slope-intercept form" is false.
• "The first equation is \(y = \frac{2}{3}x - 4\) when written in slope-intercept form" is true.
• "The second equation is \(3x + 5y = 10\) when written in slope-intercept form" is false.

Answer:

• (A) Both equations are in slope-intercept form.
• (B) Neither equation is in slope-intercept form.
• (C) The first equation is \(y = \frac{2}{3}x - 4\) when written in slope-intercept form. (Correct answer)
• (D) The second equation is \(3x + 5y = 10\) when written in slope-intercept form.