Question

At what value of x do the graphs of the equations below intersect?

2x − y = 6

5x + 10y = −10

Answer 1

x = 2

Explanation:

Given the 2 equations

2x - y = 6 → (1)

5x + 10y = - 10 → (2)

Multiplying (1) by 10 and adding to (2) eliminates the y- term.

20x - 10y = 60 → (3)

Add (2) and (3) term by term to eliminate y, that is

25x = 50 ( divide both sides by 25 )

x = 2

The value of x at the point of intersection is x = 2

Answer 2

x = 2

Explanation:

1. You would find a value of y to plug into either of the equations. For example, I chose the equation 2x - y = 6. When I set it equal to y, I got y = 2x - 6
2. Now that I know what y is equal to, I plugged it into the second equation to get 5x + 10 (2x - 6) = -10
3. You then would calculate for x.
4. Your end result should be x = 2, which is the point that the two equations intersect

This works because the two equations are set equal to each other, making them share a common value between them.

You can also plug both of these equations into a graphing calculator, and on the graph select the command to calculate the intersection.

Hope this helped!