System of Equations
Common Mistakes
System of Equations – Addition Method
How to Solve System of Equations
by the Addition Method

Line the equations by variables vertically.


Ex.
Common Mistakes

2x + 3y = 4
x − 5y = 6
Solve for one variable by adding vertically
2x + 3y = 4
− 2 x + 10 y = −12
____________
13 y = −8
−8
y=
13


Incorrect:

Correct:
Multiply one or both of the equations by a
multiple so that one variable will cancel out.
2x + 3y = 4

Ex.
− 2( x − 5 y ) = 6 equals
→ −2 x + 10 y = −12

Adding up the variables in the equations as
they are, instead of making them cancel out.
Substitute the value of “y” into either equation
and solve for “x”.
Complete Manual: ACCL 20-50\Systems of Linear Equations Review.docx
To view right click to open the hyperlink.
2x + 3y = 4
x − 5y = 6
________
3 x − 2 y = 10
2x + 3y = 4
− 2 x + 10 y = −12

Not ensuring that one of the variables cancel
out when multiplying.

Making a mistake when solving the equation.

Hint: put your answers back into the
equations, they should make both
equations true when you plug them in.
System of Equations – Substitution Method
How to solve system of equations
with the substitution method.

Solve one equations for one variable.

Common Mistakes

Hint: It doesn’t matter which equation or which variable.
2x + 3y = 4
rearranging
x − 5 y = 6  → x − 5 y = 6

x = 5y + 6

Substitute what you get into the second
equation. Then solve

Re-arranging the equation and then
substituting it back into itself. This will make
everything cancel out.
Incorrect:
2x + 3y = 4
rearranging
x − 5 y = 6  → x − 5 y = 6
Hint: Do not put the re-arranged equation back into itself, everything will
cancel out.
x = 5y + 6
2(5 y + 6) + 3 y = 4
Putting it back into itself…
10 y + 12 + 3 y = 4
13 y + 12 = 4

13 y = −8
−8
y=
13
Substitute the value of “y” into either equation
and solve for “x”.
Complete Manual: ACCL 20-50\Systems of Linear Equations Review.docx
To view right click to open the hyperlink.

5y + 6 − 5y = 6
6=6
0=0
Making a mistake when solving the equation.

Hint: put your answers back into the
equations, they should make both
equations true when you plug them in.