Warm Up #3 1. Evaluate 5x + 2y for x = 2 and y = –4. 2 ANSWER 2. Find the x and y intercepts of the equation –3x + 4y = 12. ANSWER (-4 , 0) (0 , 3)

Recall Graphing from Standard Form Graph both lines on the same graph: 3x – 2y = 6 and 5x + 2y = 10 Line 1: x int. ( , 0 ) 2   y int. ( 0 , ) -3 Line 2: x int. ( , 0 ) 2 y int. ( 0 , ) 5 Recall Graphing from Standard Form

Solve a system graphically EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 Equation 1 (2 , 0) (0 , 8) 2x – 3y = 18 Equation 2 (9 , 0) (0 , -6) SOLUTION Begin by graphing both equations, as shown at the right. From the graph, the lines appear to intersect at (3, –4). You can check this algebraically as follows.

Solve a system graphically EXAMPLE 1 Solve a system graphically Equation 1 Equation 2 4x + y = 8 2x – 3y = 18 4(3) + (–4) 8 = ? = ? 2(3) – 3( – 4) 18 = ? 12 –4 8 = ? 6 + 12 18 8 = 8 18 = 18 The solution is (3, –4).

GET THE WHITEBOARDS 

Graph both lines on the same graph: y = -2x + 4 and y = 3x - 2   They Intersect Estimate ( 1.2 , 1.8 )

Check (1.2 , 1.8) y = -2x + 4 and y = 3x - 2 1.8 = -2(1.2)+ 4 and 1.8 = 3(1.2) - 2 1.8 = -2.4 + 4 and 1.8 = 3.6 - 2 1.8 = 1.6 and 1.8 = 1.6 Not exact, but close. Many times when estimating from a graph you can only get an approximation.

Graph both lines on the same graph: 3x – 2y = 6 and 5x + 2y = 10 x int. ( , 0 ) 2   y int. ( 0 , ) -3 Line 2: x int. ( , 0 ) 2 y int. ( 0 , ) 5 They intersect at the point ( 2 , 0 )

Graph this system of linear equations, then Give the solution: y = 1/5 x + 2 y = -5/3 x + 5

Graph this system of linear equations, then Give the solution : y = 2x - 1 y = 2x + 2

Graph this system of linear equations, then Give the solution : y = 1/3 x + 2 -x + 3y = 6 Add x and divide by 3 y = 1/3 x + 2

Classwork Assignment WS 3.1 (1-11 odd and 17-20)