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Published byElvin Douglas Modified over 8 years ago

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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.

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

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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.

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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!!!!

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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.

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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.

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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

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

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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.

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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

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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

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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.

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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

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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

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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.

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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----

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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

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

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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.

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

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(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

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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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