The two sides of the equation will be equal if the quantities inside the absolute value signs are equal or equal with opposite signs.

From this, you get two equations.

or

This is a difference of squares. The difference of squares formula is _a_2 – _b_2 = (a + b)(a – b).

In this problem, a = 6_x_ and b = 7_y_:

36_x_2 – 49_y_2 = (6_x_ + 7_y_)(6_x_ – 7_y_)

To solve this equation you will plug the second equation straight into the first one by substituting what is written there for .

You will then get:

From here you need to simplify by combining like terms:

Bring the over by addition:

Then divide both sides by to get:

You will then take this value of and plug it into either equation.

To find the solution isolate the variable on one side of the equation.

To check to see if this is the correct solution, plug the value of x back into the equation and solve:

To find the solution isolate the variable on one side of the equation.

To check to see if this is the correct solution, plug the value of x back into the equation and solve:

We can rewrite the first equation as:

If we substitute this new value for into the second equation we get:

Simplify.

Combine like terms

Solve for

Now substitute this value into either of the original equations:

For elimination you need to get one variable by itself by cancelling the other out. In this equation this is best done by getting rid of . You can multiply whichever equation you would like to, but multiply it by to get

then add the equations together

which, simplified, is

divied by to get

Then plug back into any equation for the x value

Solve for to get

For elimination you need to get one variable by itself by cancelling the other out. In this equation this is best done by getting rid of . You can multiply whichever equation you would like to, but multiply it by to get

then add the equations together

which, simplified, is

divied by to get

Then plug back into any equation for the x value

Solve for to get

The first step is to set the two equations equal to each other, since at the point of intersection, they will be. To do this more easily, convert each equation into slope-intercept form.

First equation:

State equation

Add to both sides.

Divide both sides by .

Second equation:

State equation

Symmetric Property of Identity

Now, since each equation equals , the equations also equal each other (for the point of intersection). By solving for , therefore, we can

State equation.

Add to both sides.

Subtract from both sides.

Divide both sides by (or multiply both sides by ).

So, the -coordinate of our intersection is . To find the -coordinate, plug this result back into one of the original equations.

State your chosen equation.

Substitute the value of .

Multiply.

Subtract.

So, the coordinates where the two lines intersect are .

We can rewrite the first equation as:

If we substitute this new value for into the second equation we get:

Simplify.

Combine like terms

Solve for

Now substitute this value into either of the original equations: