,

Multiply each equation by the value that makes the coefficients of opposite.

Simplify .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Multiply by .

Simplify .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Multiply by .

Add the two equations together to eliminate from the system.

Since , the equations intersect at an infinite number of points.

Infinite number of solutions

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

The solution is the set of ordered pairs that make true.

The result can be shown in multiple forms.

Point Form:

Equation Form:

Solve by Addition/Elimination 2x+6y=10 , 3x+9y=15