Question

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

Line C: y = x + 14
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why? (5 points)

Group of answer choices

(6, 20), because the point does not lie on any axis

(3, 11), because the point lies between the two axes

(3, 11), because one of the lines passes through this point

(6, 20), because both lines pass through this point

Answer 1

y=x+14 line 1

y=3x+2 line 2

These are both the equation of lines written in slope intercept form

y=mx+b where m is the slope and the point (0,b) is the y intercept.

The first line has a slope of m=1. The 2nd line has a slope of m=3

Since these lines have different slopes, they are not parallel, thus they will cross at some point. What you have to determine is where the lines cross, which will be a point (x,y) that is on both lines.

We already have y solved in terms of x from either equation so we can use substitution to solve the system.

Since y=x+14 from line 1, put x+14 in place of y in the equation of line 2.

x+14=3x+2

solve for x.

Subtract x from both sides...

14= 3x-x+2

14=2x+2

subtract 2 from both sides

14-2=2x

12=2x

divide both sides by 2

6=x

We now have the x value of the common point. Plug the value 6 in for x in one of the original equations and solve for y.

y=6+14

y=20

These two lines cross at the point (6,20) which is a point the two lines have in common.

Hope I helped (SharkieOwO)