Question

consider the system of linear equations.
$2y = x + 10$
$3y = 3x + 15$
which statements about the system are true? check all that apply
□ the system has one solution.
□ the system graphs parallel lines.
□ both lines have the same slope.
□ both lines have the same y-intercept.
□ the equations graph the same line.
□ the solution is the intersection of the 2 lines.

Explanation:

Step1: Rewrite to slope-intercept form

First equation: $2y = x + 10$ → $y = \frac{1}{2}x + 5$
Second equation: $3y = 3x + 15$ → $y = x + 5$

Step2: Compare slopes and intercepts

Slope of first line: $\frac{1}{2}$, y-intercept: $5$
Slope of second line: $1$, y-intercept: $5$

Step3: Analyze system properties

Lines have different slopes, so they intersect at one point (one solution). They share the same y-intercept, are not parallel, and do not graph the same line.

Answer:

• The system has one solution.
• Both lines have the same y-intercept.
• The solution is the intersection of the 2 lines.