Download Name: Date: Mr. Art Period: Solving Linear Equations, Linear

Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Solving Linear Equations, Linear Systems Algebraically
I. Solving Linear Equations
Steps:
* Only do steps 1, 2, or 3 if possible, if not start at step 4!
1) “Clear” Parentheses (by Distributing when necessary)
 Multiply the term on outside of the
2) Combine Like Terms
 Add or Subtract terms that have the
same variable AND the same exponent
3) Variables on Both Sides of the Equal Sign
 “Undo” smaller term with variable on one side of the
equal sign from the larger term with variable on the
other side of the equal sign.
 By the Inverse (opposite) Addition or Subtraction
4) “Undo” the Constant
 By the Inverse (opposite) Addition or Subtraction
 Constant number alone (stays the same)
5) “Undo” the Coefficient
 By the Inverse (opposite) Division or Multiplication
 Coefficient number with variable
6) Check (your solution)
1) Rewrite
2) Replace
3) Recalculate
 No Distributing, Combining Like Terms, or Inverse
operations in Check.
 Simply plug in value to determine if both sides of the
equation are equal.
Reminder:
 Negative (-) is the same as Subtraction (-)
 Positive (+) is the same as Addition (+)
Ex. 5 – x = 12 is the same as – x + 5 = 12
Ex. 5 + x = 12 is the same as x + 5 = 12
 An equation is like a scale…whatever you do to one side, must also be done to the other side
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II. Literal Equations: equations with multiple variables
*Solve 10 = 2x + 4 to help you
with the steps.
II. Systems Algebraically
1) Elimination Method:
Steps: 1) Eliminate one of the variables ( same sign = subtract, different signs = add)
2) Solve for the variable you didn't eliminate
3) Plug the variable you just solved for back into one of the equations to find the other.
a)
b)
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c)
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2) Substitution Method
Steps:
1) When one of the equations is equal to one of the variables (like how the example below
has an equation already equal to x),
2) Plug in what is equal to that variable (4y) into the other equation in place of that original
variable (4y will replace x in the 5x - 3y = 17 equation).
3) The result will be that one variable will be eliminated and you will solve for the other.
4) Once you solve for the first variable, plug the answer into one of the two equations then
solve for the second variable.
a)
b)
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