Question

At which point on the coordinate grid do the graphs of the equations 8x+2y=14and -4x-y=6 intersect?

Answer 1

The two equations do not intersect.

Explanation:

The intersection point of two equations can be found using 3 different methods. These methods are:

• Substitution
• Elimination
• Graphing

Let's solve it using elimination.

Solve Using Elimination

To solve the system of equations using elimination, we must first make one variable in both of the equations equivalent.

In order to do this, we need to multiply the second equation by 2.

`2(-4x-y)=2(6)\\-8x-2y=12` (make sure that both sides have been multiplied by 2)

Now, we can add the two equations:

`8x+2y+(-8x-2y)=14+12\\8x+2y-8x-2y=26`Combine like terms

`0 = 26`

0 cannot be equivalent to 26, thus this equation has no solutions. If we graphed these two equations, we would see that the two lines are parallel.