consider the system of linear equations. 2y = x + 10 3y = 3x + 15 which statements about the system are…

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.

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.

Answer

Explanation:

Step1: Rewrite equations in slope - intercept form

The first equation $2y=x + 10$ can be rewritten as $y=\frac{1}{2}x+5$ by dividing both sides by 2. The second equation $3y=3x + 15$ can be rewritten as $y=x + 5$ by dividing both sides by 3.

Step2: Analyze slope and y - intercept

For $y=\frac{1}{2}x+5$, the slope $m_1=\frac{1}{2}$ and the y - intercept $b_1 = 5$. For $y=x + 5$, the slope $m_2=1$ and the y - intercept $b_2 = 5$. Since the y - intercepts are the same ($b_1=b_2 = 5$) and the slopes are different ($m_1\neq m_2$), the lines intersect at the y - intercept. The solution of a system of linear equations is the intersection of the two lines.

Answer:

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