1. System of Equations Solve by Substitution

2. A System of Equations:  Consists of two linear equations  We want to find out information about the two lines: –The exact location (x, y) where they cross –If the two equations are the same line (infinite solutions) –If they are parallel, then they don’t cross (no solution)

3. Ex 1 Choose which variable you will solve for first. (here y is already solved for in 2 nd equation) Replace that variable (y) in 1 st equation with what it (y) is equal to from the 2 nd equation. Now you should have two x’s in the same equation. Just solve for x Plug that answer into one of the original equations and solve for y Answer: (2, 10)

4. Ex 2 Choose which variable you will solve for first. (here y is already solved for in 2 nd equation) Replace that variable (y) in 1 st equation with what it (y) is equal to from the 2 nd equation. Now you should have two x’s in the same equation. Just solve for x Plug that answer into one of the original equations and solve for y Answer: (-3, -12)

5. Ex 3 Choose which variable you will solve for first. (here x is already solved for in 2 nd equation) Replace that variable (x) in 1 st equation with what it (x) is equal to from the 2 nd equation. Now you should have two y’s in the same equation. Just solve for y Plug that answer into one of the original equations and solve for x Answer: (2, 5)

6. Ex 4 Choose which variable you will solve for first. (here x is already solved for in 2 nd equation) Replace that variable (x) in 1 st equation with what it (x) is equal to from the 2 nd equation. Now you should have two y’s in the same equation. Just solve for y Plug that answer into one of the original equations and solve for x Answer: (-1, -2)

7. Ex 5 Choose which variable you will solve for first. (here y is already solved for in 2 nd equation) Replace that variable (y) in 1 st equation with what it (y) is equal to from the 2 nd equation. Now you should have two x’s in the same equation. Just solve for x Plug that answer into one of the original equations and solve for y Answer: (-2, 1)

8. Ex 6 Choose which variable you will solve for first. (here y is already solved for in 2 nd equation) Replace that variable (y) in 1 st equation with what it (y) is equal to from the 2 nd equation. Now you should have two y’s in the same equation. Just solve for y Plug that answer into one of the original equations and solve for x Answer: (-5, 3)