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 equations in slope-intercept form

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

Step2: Identify slopes and y-intercepts

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

Step3: Analyze system properties

Slopes are different, so lines intersect at one point (one solution). Parallel lines require equal slopes (not true here). Only y-intercepts are equal. The single solution is the intersection point.

Answer:

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