Learning Target I can solve systems of equations

Learning Target: I can solve systems of equations by graphing.

WARM-UP Graph: Solve for y: y = -3/4 x + 3

VOCABULARY New Word system of equations solution of a system coincident Visual Clue x+y=9 x – y = -5 Definition { more than one equation More than one equation Point that is true for all equations in the system Two lines that have the same slope and same y-intercept

QUICK GAME. . . CLUE – WHAT TWO NUMBERS… CLUE #1: Two numbers have a sum of 9. Possibilities: 1, 8 0, 9 8. 5, 0. 5 7, 2 5, 4 – 1, 10 CLUE #2: The first number minus the second number equals 5. 7 2 Write an equation for the answer. x = _____ y = _____ or (____, ____)

To solve a system of equations by graphing: Step 1: Equations should be in slope-intercept form. _______ Rewrite equation if needed. Graph Step 2: ____ both lines. Step 3: Find the coordinates of the point where the two lines intersect ______. (touch)

EXAMPLE #1 Find the coordinates of the point where the lines touch. (0, 3) Solution: _____ or x =0___, y =3___

EXAMPLE #2 Find the coordinates of the point where the lines touch. (2, – 1) – 1____ Solution: ____ or x =2___, y =

EXAMPLE #3 Paralle l Find the coordinates of the point where the lines touch. Solution: ________ No solution

EXAMPLE #4 – 4 x 4 x – 2 y = – 4 x +14 2 2 2 They overlap! The lines are coincident (identical) Solution: _________ Infinitely many

YOUR TURN! a) b) c) One Parallel lines = No solution Same line = Coincident = Infinitely many

ARE YOU A MASTER? Draw a picture for each type of solution: No solution One Solution Infinitely Many