Question

solving a system of linear equations
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

Slopes: $\frac{1}{2}
eq 1$; y-intercepts: both $5$

Step3: Analyze system properties

Distinct slopes → lines intersect once; one unique solution.

Answer:

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