Question

Two lines, C and D, are represented by the equations given below:

Line C: y = x + 10
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why?
A) (5, 17), because one of the lines passes through this point
B) (5, 17), because the point lies between the two axes
C) (4, 14), because the point does not lie on any axis
D) (4, 14), because both lines pass through this point

Answer 1

The solution to the system of equations represented by Line C (y = x + 10) and Line D (y = 3x + 2) is found by setting the two equations equal to each other. The solution to where they intersect is (4, 14), which corresponds to option D, because both lines pass through this point.

Step-by-step explanation:

The student is asking about the solution to the system of equations represented by Line C (y = x + 10) and Line D (y = 3x + 2). To find the solution, we need to set the equations equal to each other since the solution is the point where both lines intersect. After setting them equal, we solve for x:

x + 10 = 3x + 2

10 - 2 = 3x - x

8 = 2x

x = 4

Now that we have the value of x, we can substitute it back into either equation to find y:

y = 4 + 10 = 14

Therefore, the point of intersection is (4, 14) and both lines pass through this point. This corresponds to option D: (4, 14), because both lines pass through this point.