# Solve Systems By Substitution (Harder Version)

Systems of Equations

# Solve Systems By Substitution (Harder Version)

Created 3 years ago

Duration 0:08:08
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Slide Content
1. ### 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. ### 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. ### 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. ### 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. ### 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.