Solve Systems By Substitution (Harder Version)

Systems of Equations
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Solve Systems By Substitution (Harder Version)

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  1. 2) Solve the system using substitution

    Slide 1 - 2) 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 -3y
    • x = -3y + 7
    • 4x – 2y = 0
    • 4(-3y + 7) – 2y = 0
  2. 2) Solve the system using substitution

    Slide 2 - 2) Solve the system using substitution

    • 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
  3. 2) Solve the system using substitution

    Slide 3 - 2) Solve the system using substitution

    • 3y + x = 7
    • 4x – 2y = 0
    • Step 5: Check your solution.
    • (1, 2)
    • 3(2) + (1) = 7
    • 4(1) – 2(2) = 0
    • When is solving systems by substitution easier to do than graphing?
    • When only one of the equations has a variable already isolated (like in example #1).
  4. If you solved the first equation for x, what would be substituted into the bottom equation.

    Slide 4 - If you solved the first equation for x, what would be substituted into the bottom equation.

    • 2x + 4y = 4
    • 3x + 2y = 22
    • -4y + 4
    • -2y + 2
    • -2x + 4
    • -2y+ 22
  5. 3) Solve the system using substitution

    Slide 6 - 3) Solve the system using substitution

    • 2x + y = 4
    • 4x + 2y = 8
    • Step 1: Solve an equation for one variable.
    • Step 2: Substitute
    • The first equation is
    • easiest to solved for y!
    • y = -2x + 4
    • 4x + 2y = 8
    • 4x + 2(-2x + 4) = 8
    • Step 3: Solve the equation.
    • 4x – 4x + 8 = 8
    • 8 = 8
    • This is also a special case.
    • Does 8 = 8? TRUE!
    • When the result is TRUE, the answer is INFINITELY MANY SOLUTIONS.
  6. What does it mean if the result is “TRUE”?

    Slide 7 - What does it mean if the result is “TRUE”?