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Dr. Fowler CCM Solving Systems of Equations By Substitution – Harder

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Solving a system of equations by substitution Step 1: Solve an equation for one variable. Step 2: Substitute Step 3: Solve the equation. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Put the equation solved in Step 1 into the other equation. Get the variable by itself. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations. ALREADY IN NOTES – Read Only for Review

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1) Solve the system using substitution 3y + x = 7 4x – 2y = 0 Step 1: Solve an equation for one variable. Step 2: Substitute It is easiest to solve the first equation for x. 3y + x = 7 -3y x = -3y + 7 4x – 2y = 0 4(-3y + 7) – 2y = 0

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3y + x = 7 4x – 2y = 0 Step 4: Plug back in to find the other variable. 4x – 2y = 0 4x – 2(2) = 0 4x – 4 = 0 4x = 4 x = 1 Step 3: Solve the equation. -12y + 28 – 2y = 0 -14y + 28 = 0 -14y = -28 y = 2 1) Solve the system using substitution

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3y + x = 7 4x – 2y = 0 Step 5: Check your solution. (1, 2) 3(2) + (1) = 7 4(1) – 2(2) = 0 1) Solve the system using substitution Answer is (1,2)

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2) Solve the following system using the substitution method. 3x – y = 6 and – 4x + 2y = –8 STEP 1 – Solve the first equation for y is easiest, 3x – y = 6 –y = –3x + 6 (subtract 3x from both sides) y = 3x – 6 (multiply both sides by – 1) STEP 2 – Substitute this value for y in the OTHER equation. –4x + 2y = –8 –4x + 2(3x – 6) = –8 (replace y to other equation) –4x + 6x – 12 = –8 (use the distributive property) 2x – 12 = –8 (simplify the left side) 2x = 4 (add 12 to both sides) x = 2 (divide both sides by 2) CONTINUED >

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STEP 3 – To get y, substitute x = 2 into either original equation. The easiest is the one that was already solved for y. y = 3x – 6 = 3(2) – 6 = 6 – 6 = 0 y = 0 We have now found x & y. Answer is (2, 0)

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EXAMPLE 3 TRUE – The answer is infinitely many solutions Solve the system by the substitution method. Solve first for x:Substitute:

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EXAMPLE 4 Use substitution to solve the system. Solve first for x: Substitute into other equation: To get X, substitute y you found into equation already solved for X:

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Example #5: x + y = 10 5x – y = 2 Step 1: Solve one equation for one variable. x + y = 10 y = -x +10 Step 2: Substitute into the other equation. 5x - y = 2 5x -(-x +10) = 2

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x + y = 10 5x – y = 2 5x -(-x + 10) = 2 5x + x -10 = 2 6x -10 = 2 6x = 12 x = 2 Step 3: Simplify and solve the equation.

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x + y = 10 5x – y = 2 Step 4: Substitute back into either original equation to find the value of the other variable. x + y = 10 2 + y = 10 y = 8 Solution to the system is (2,8).

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Excellent Job !!! Well Done

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Stop Notes Do Worksheet

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