# objective I Can state the first step for solving systems. I Can solve systems of equations by graphing, substitution or elimination.

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objective I Can state the first step for solving systems. I Can solve systems of equations by graphing, substitution or elimination.

BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION

Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Step 2: Do the graphs intersect? Step 3: Check your solution. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! This is the solution! LABEL the solution! Substitute the x and y values into both equations to verify the point is a solution to both equations.

Graphing is not the only way to solve a system of equations. It is not really the best way because it has to be graphed perfectly and some answers are not integers. SOOOO We need to learn another way!!!!

Solving a system of equations by elimination using multiplication. Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Multiply the equations and solve. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.

Solve: by ELIMINATION x + y = 12 -x + 3y = -8 We need to eliminate (get rid of) a variable. The x’s will be the easiest. So, we will add the two equations. 4y = 4 Divide by 4 y = 1 THEN---- Like variables must be lined under each other.

X +Y = 12 (11,1) Substitute your answer into either original equation and solve for the second variable. Answer Now check our answers in both equations------ x + 1 = 12 -1 -1 x = 11

X + Y =12 11 + 1 = 12 12 = 12 -x + 3y = -8 -11 + 3(1) = -8 -11 + 3 = -8 -8 = -8

Solve: by ELIMINATION 5x - 4y = -21 -2x + 4y = 18 We need to eliminate (get rid of) a variable. The y’s be will the easiest.So, we will add the two equations. 3x = -3 Divide by 3 x = -1 THEN---- Like variables must be lined under each other.

5X - 4Y = -21 (-1, 4) Substitute your answer into either original equation and solve for the second variable. Answer Now check our answers in both equations------ 5(-1) – 4y = -21 -5 – 4y = -21 5 -4y = -16 y = 4

5x - 4y = -21 5(-1) – 4(4) = -21 -5 - 16 = -21 -21 = -21 -2x + 4y = 18 -2(-1) + 4(4) = 18 2 + 16 = 18 18 = 18

Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45 We need to eliminate (get rid of) a variable. The y’s will be the easiest. So, we will add the two equations. 7x = -14 Divide by 7 x = -2 THEN---- Like variables must be lined under each other.

2X + 7Y = 31 (-2, 5) Substitute your answer into either original equation and solve for the second variable. Answer Now check our answers in both equations------ 2(-2) + 7y = 31 -4 + 7y = 31 4 7y = 35 y = 5

2x + 7y = 31 2(-2) + 7(5) = 31 -4 + 35 = 31 31 = 31 5x – 7y = - 45 5(-2) - 7(5) = - 45 -10 - 35 = - 45 - 45 =- 45

Solve: by ELIMINATION x + y = 30 x + 7y = 6 We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable. If one of the x’s was negative, it would be eliminated when we add. So we will multiply one equation by a – 1. Like variables must be lined under each other.

X + Y = 30 X + 7Y = 6() X + Y = 30 -X – 7Y = - 6 Now add the two equations and solve. -6Y = 24 - 6 Y = - 4 THEN----

X + Y = 30 (34, - 4) Substitute your answer into either original equation and solve for the second variable. Answer Now check our answers in both equations------ X + - 4 = 30 4 X = 34

x + y = 30 34 + - 4 = 30 30 = 30 x + 7y = 6 34 + 7(- 4) = 6 34 - 28 = 6 6 = 6

Solve: by ELIMINATION x + y = 4 2x + 3y = 9 We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable. If there was a –2x in the 1 st equation, the x’s would be eliminated when we add. So we will multiply the 1st equation by a – 2. Like variables must be lined under each other.

X + Y = 4 2X + 3Y = 9 -2X - 2 Y = - 8 2X + 3Y = 9 Now add the two equations and solve. Y = 1 THEN---- () -2

(3,1) Substitute your answer into either original equation and solve for the second variable. Answer Now check our answers in both equations------ X + Y = 4 X + 1 = 4 - 1 -1 X = 3

x + y = 4 3 + 1 = 4 4 = 4 2x + 3y = 9 2(3) + 3(1) = 9 6 + 3 = 9 9 = 9

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