ALGEBRA II SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS

1) Solve by graphing. 2x + y = 8 3x – 2y = -2 Solve for y. y = -2x + 8 Find the intercepts. x-int : -2/3 y-int : 1 The point of intersection is (2, 4) Note that 2(2) + 4 = 8 and 3(2) – 2(4) = -2

2) Solve by substitution. 2x + y = 8 3x – 2y = -2 Look for the equation where solving for x or for y is easiest. Solve for y in the top equation. y = -2x + 8 Next, substitute into the other equation and solve. 3x – 2y = -2 3x – 2(-2x + 8) = -2 3x + 4x – 16 = -2 7x – 16 = -2 7x = 14 x = 2 Substitute 2 for x for find y. y = -2(2) + 8 = 4 Therefore, the answer is (2, 4)

3) Solve using elimination (linear combination) 2x + y = 8 3x – 2y = -2 The goal is to make opposites for one of the variables and add the equations together. Multiply the top equation by 2 to make 2y on top to go along with the -2y on bottom. 2 (2x + y) = 8 2 3x – 2y = -2 4x + 2y = 16 3x – 2y = -2 7x = 14 x = 2 Substitute 2 for x into either original equation to find y. 2(2) + y = y = 8 y = 4 Therefore, the answer is (2, 4)

METHODS FOR SOLVING SYSTEMS OF EQUATIONS : 1)Graphing 2)Substitution 3)Elimination (linear combination) 4)???? 5)????

Solve using the method of your choice. 4) 3x – 7y = 31 2x + 5y = 11 5) 4x + 3y = 10 5x - y = 22

6) 2x – 3y = 12 y = -2x + 4 Just in case you want it!!

7) y = x + 1 y = x – 2 8) 2x – 4y = -16 -x + 2y = 8 If the variables cancel true statement infinite solutions same lines false statement no solutions Parallel lines

8) 4x – 3y = 11 5x – 6y = 9 9)

NAMES FOR SYSTEMS OF EQUATIONS Inconsistent equations Parallel lines Dependent equations Coincidental lines Independent equations Intersecting lines