Download Solving Systems of Equations by Substitution Notes

Solving Systems of Equations by Substitution Notes:
Solving for a system of equations means:
Finding where 2 lines meet, where they share an ordered
pair, where they both are “true”. We can find solution by
graphing, substitution or elimination methods.
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Basic Steps for Solving by Substitution:
Step 1: Solve one of the equations for a single variable
Pick the easier equation.
The goal is to get y= , x= , a= , etc.
Step 2: Substitute
Put the solution to the variable from step 1 into
the other equation in place of variable
Step 3: Solve the Equation
Get the variable by itself in the new equation
Step 4: Plug back in to find the other variable
Substitute the value of the variable into one of
the equations (pick easier one) and solve
Step 5: Check your solution
Substitute the ordered pair
(solutions you found) into BOTH equations
Example: Solve for this system of equations:
2x + y = 5
–3x + 2y = 17
Step 1: Solve the first equation for y: 2x + y = 5
(Move the 2x to other side)
–2x
–2x
Re-write the equation
+ y = 5 – 2x
Step 2: Substitute for y in other eq:
Replace y with (5 – 2x)
–3x + 2y = 17
–3x + 2(5 – 2x) = 17
Step 3: Solve (distribute first)
(combine like terms –3x –4x)
Get variable alone (move 10)
Re-write (17 –10)
Get variable alone (move –7)
Re-write
–3x + 10 – 4x = 17
–7x + 10 = 17
–10 –10
–7x = 7
÷ –7 ÷ –7
x = –1
Step 4: Plug in to find y
Replace x with (– 1)
Solve
–3x + 2y = 17
–3(– 1) + 2y = 17
3 + 2y = 17
–3
–3
2y = 14
÷2 ÷2
y=7
Step 5: Check the solution (–1, 7)
( x ,y)
2x + y = 5
2(–1) + 7 = 5
5=5 
–3x + 2y = 17
–3(–1) + 2(7) = 17
3 + 14 = 17
17 = 17 
Check the solution (–1, 7)