Solve Systems By Substitution (Easy Version)

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Systems of Equations

Slide 1  Objective
 The student will be able to:
 solve systems of equations using substitution.
 SOL: A.4e
 Designed by Skip Tyler, Varina High School
 Modified by Mr. Burns

Slide 2  Solving Systems of Equations
 These notes show how to solve the system algebraically using SUBSTITUTION.

Slide 3
 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.

Slide 4  1) Solve the system using substitution
 x + y = 5
 y = 3 + x
 Step 1: Solve an equation for one variable.
 Step 2: Substitute
 The second equation is
 already solved for y!
 x + y = 5x + (3 + x) = 5
 Step 3: Solve the equation.
 2x + 3 = 5
 2x = 2
 x = 1

Slide 5  1) Solve the system using substitution
 x + y = 5
 y = 3 + x
 Step 4: Plug back in to find the other variable.
 x + y = 5
 (1) + y = 5
 y = 4
 Step 5: Check your solution.
 (1, 4)
 (1) + (4) = 5
 (4) = 3 + (1)
 The solution is (1, 4). What do you think the answer would be if you graphed the two equations?

Slide 6  Which answer checks correctly?
 3x – y = 4
 x = 4y  17
 (2, 2)
 (5, 3)
 (3, 5)
 (3, 5)

Slide 7  3) Solve the system using substitution
 x = 3 – y
 x + y = 7
 Step 1: Solve an equation for one variable.
 Step 2: Substitute
 The first equation is
 already solved for x!
 x + y = 7
 (3 – y) + y = 7
 Step 3: Solve the equation.
 3 = 7
 The variables were eliminated!!
 This is a special case.
 Does 3 = 7? FALSE!
 When the result is FALSE, the answer is NO SOLUTIONS.