Dr Fowler CCM Solving Systems of Equations By
Dr. Fowler CCM Solving Systems of Equations By Substitution – Harder
Solving a system of equations by substitution Step 1: Solve an equation for one variable. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Step 2: Substitute Put the equation solved in Step 1 into the other equation. Step 3: Solve the equation. Get the variable by itself. Step 4: Plug back in to find the other variable. Substitute the value of the variable into the equation. Step 5: Check your solution. Substitute your ordered pair into BOTH equations. ALREADY IN NOTES – Read Only for Review
1) Solve the system using substitution 3 y + x = 7 4 x – 2 y = 0 Step 1: Solve an equation for one variable. Step 2: Substitute It is easiest to solve the first equation for x. 3 y + x = 7 -3 y x = -3 y + 7 4 x – 2 y = 0 4(-3 y + 7) – 2 y = 0
1) Solve the system using substitution 3 y + x = 7 4 x – 2 y = 0 Step 3: Solve the equation. -12 y + 28 – 2 y = 0 -14 y + 28 = 0 -14 y = -28 y=2 Step 4: Plug back in to find the other variable. 4 x – 2 y = 0 4 x – 2(2) = 0 4 x – 4 = 0 4 x = 4 x=1
1) Solve the system using substitution 3 y + x = 7 4 x – 2 y = 0 Step 5: Check your solution. Answer is (1, 2) 3(2) + (1) = 7 4(1) – 2(2) = 0 (1, 2)
2) Solve the following system using the substitution method. 3 x – y = 6 and – 4 x + 2 y = – 8 STEP 1 – Solve the first equation for y is easiest, 3 x – y = 6 –y = – 3 x + 6 (subtract 3 x from both sides) y = 3 x – 6 (multiply both sides by – 1) STEP 2 – Substitute this value for y in the OTHER equation. – 4 x + 2 y = – 8 – 4 x + 2(3 x – 6) = – 8 (replace y to other equation) – 4 x + 6 x – 12 = – 8 (use the distributive property) 2 x – 12 = – 8 (simplify the left side) 2 x = 4 (add 12 to both sides) x=2 (divide both sides by 2) CONTINUED >
STEP 3 – To get y, substitute x = 2 into either original equation. The easiest is the one that was already solved for y. y = 3 x – 6 = 3(2) – 6 = 6 – 6 = 0 y=0 We have now found x & y. Answer is (2, 0)
EXAMPLE 3 Solve the system by the substitution method. Solve first for x: TRUE – The answer is Substitute: infinitely many solutions
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:
Example #5: x + y = 10 5 x – y = 2 Step 1: Solve one equation for one variable. x + y = 10 y = -x +10 Step 2: Substitute into the other equation. 5 x - y = 2 5 x -(-x +10) = 2
x + y = 10 5 x – y = 2 Step 3: Simplify and solve the equation. 5 x -(-x + 10) = 2 5 x + x -10 = 2 6 x = 12 x=2
x + y = 10 5 x – 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).
Excellent Job !!! Well Done
Stop Notes Do Worksheet
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