Lesson 10 Solving Systems with Elimination Part 2

7x+3y=50

7x−3y=50

5x+4y=2x−7y

3x−11y=-2

3x+11y=-2

Because 13x−13y=-26 is the product of the two equations in the system of equations, it the must share a solution with the system of equations.

The three equations all have the same slope but different y-intercepts. Equations with the same slope but different y-intercepts always share a solution.

Because 10x−3y is equal to 29, I can add 10x−3y to the left side of -3x+10y=55 and add 29 to the right side of the same equation. Adding equivalent expressions to each side of an equation does not change the solution to the equation.

Because -3x+10y is equal to 55, I can subtract -3x+10y from the left side of 10x−3y=29 and subtract 55 from its right side. Subtracting equivalent expressions from each side of an equation does not change the solution to the equation.

-2x−4y=8

-2x+6y=8

4x−4y=16

4x+4y=16

2x−6y=-8