Question

Do the lines given by the equations below intersect at the point (4,-6)? Explain why or why not.

2x - y = 14
x - 3y = 22

A. No, (4, -6) is not a point of intersection because it is not a solution to x - 3y = 22.
B. Yes, (4, -6) is a point of intersection because it is a solution to both equations.
C. No, (4 ,-6) is not a point of intersection because it is not a solution to 2x - y = 14.
D. No, (4, -6) is not a point of intersection because it is not a solution to either equations. ​

Answer 1

B. Yes, (4, -6) is a point of intersection because it is a solution to both equations.

Explanation:

In order to find if a certain point exists on a line or not, we can simply substitute in the values, and see if the result is valid. Here we are given the point (4,-6), this means our x=4 and our y=-6. If this point lies on a line, then substituting in the values should result in a valid equation. Let's try the first one:

2x-y=14

2(4)-(-6)=14

8+6=14

14=14

This equation is valid which means the point (4,-6) is indeed a point on the first given line equation.

Now for the second one:

x-3y=22

(4)-3(-6)=22

4+18=22

22=22

This is also a valid equation meaning the point (4,-6) also exists on the second line equation. Since this point exists on both lines, they will intersect each other on a graph. Therefore the best answer here is B. Yes, (4, -6) is a point of intersection because it is a solution to both equations.

Hope this helped!