Question

What is true concerning the lines graphed by the system of equations shown below?​

Answer 1

Answer:

H

Step-by-step explanation:

Solve each equation for y.

First equation:

8x + 6 = 2y

2y = 8x + 6

y = 4x + 3

This line has y-intercept 3, and slope 4.

Second equation:

12x - 3 = 3y

3y = 12x - 3

y = 4x - 1

This line has y-intercept -1 and slope 4.

Since the two lines have the same slope and different y-intercepts, they are parallel lines.

Answer: H

Answer 2

Answer:

The correct answer is H.

Step-by-step explanation:

In order to solve this exercise we have two paths. The first one uses less calculation than the second.

First way of solution: Isolate the variable $y$ in the right hand side of each equation. To do this you only need to divide the first equation by 2, and then divide the second equation by 3. Thus, you will obtain $4x+3=y$ and $4x-1=y$.

Now, notice that both lines have the same slope, so they are parallel. But before to give a definite answer we need to check if both lines are the same or not. Evaluate at $x=0$, in the first equation you have $y=3$ and in the second one $y=-1$. As they have different intercepts with the X-axis, they parallel.

Second way of solution: Solve the system of equations. Isolate $y$ in the first equation:

$4x+3=y$.

Then, substitute this expression in the second equation:

$12x-3=3(4x+3)$

$12x-3=12x +9$.

Which is equivalent to $0=9+3$ and this is impossible. Hence, the system of equations has no solution and the lines are parallel.