Solve Systems By Substitution (Easy Version)

Systems of Equations
1.0x

Solve Systems By Substitution (Easy Version)

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  1. Objective

    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
  2. Solving Systems of Equations

    Slide 2 - Solving Systems of Equations

    • These notes show how to solve the system algebraically using SUBSTITUTION.
  3. 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.
  4. 1) Solve the system using substitution

    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
  5. 1) Solve the system using substitution

    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?
  6. Which answer checks correctly?

    Slide 6 - Which answer checks correctly?

    • 3x – y = 4
    • x = 4y - 17
    • (2, 2)
    • (5, 3)
    • (3, 5)
    • (3, -5)
  7. 3) Solve the system using substitution

    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.