Question

At what point do y=2x+(-6) and y=1/2x+3 cross?

Answer 1

To solve this, set both equations equal to each other. You’re able to do so because they both equal y.

Now we have:

2x - 6 = 1/2x + 3

To solve, isolate the x variable by rearranging the equation and combining like terms:

2x - 1/2x = 3 + 6
3/2x = 9

Now divide by 3/2 by multiplying 9 by the reciprocal fraction 2/3:

x = 18/3

x = 6

This is the value of the x-coordinate of the point at which the two lines intersect. Yo find the ordered pair, plug in this value of x into either equation and solve for y, they should equal the same number:

Let’s use y = 1/2x + 3:

y = 1/2(6) + 3

y = 3 + 3

y = 6

Let’s check the other equation:

y = 2(6) - 6

y = 12 - 6

y = 6

We can for sure say the y-coordinate is 6. This gives you an ordered pair of:

(6,6)

(6,6) is the point at which the two lines intersect!

Answer 2

The point of intersection is (6, 6).


To find the point where two lines intersect, we need to solve the system of equations:

y = 2x - 6 (equation 1)

y = 1/2x + 3 (equation 2)

We can solve this system by setting the two expressions for y equal to each other:

2x - 6 = 1/2x + 3

Multiplying both sides by 2 to eliminate the fraction, we get:

4x - 12 = x + 6

Subtracting x and adding 12 to both sides, we get:

3x = 18

Dividing by 3, we get:

x = 6

Now we can plug this value of x into either equation to find the corresponding y-coordinate. Let's use equation 1:

y = 2(6) - 6 = 6

Therefore, the point of intersection is (6, 6).