Solving Systems Of Equations With Fractions Or Decimals


In these lessons, we help Algebra 1 students learn to solve systems of linear equations with fractions.

Related Pages
Solving Systems of Equations or Simultaneous Equations using algebra
Solving Simultaneous Equations Using Matrices
More Lessons On Matrices
Algebra Lessons




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How To Solve Systems Of Equations With Fractions?

When a system includes an equation with fractions as coefficients:
Step 1. Eliminate the fractions by multiplying each side of the equation by a common denominator.
Step 2: Solve the resulting system using the addition method, elimination method, or the substitution method.

The following diagrams show how to solve systems of equations using the Substitution Method and the Elimination Method.

System of Equations Substitution

System of Equations Elimination

Systems of Equations with Fractions

Students learn to solve systems of linear equations that involve fractions. Students also learn to solve linear systems of equations by the method of their choice using the following rules: if one of the variables cancels out when the equations are added together, then use addition, and if a variable is already isolated in one of the equations, then use substitution.

Example:
Solve the following systems of equations
y = 1/3 x - 1
3x - 2y = 4




Solving a System Involving Fractions with Substitution

How to solve a system of 2 equations with 2 variables involving fractions using substitution?

Example:
y = -3/4 x + 12
y = 1/3 x - 2

Solving a System Involving Fractions with Elimination

How to solve a linear system by the process of elimination where the equations contain fractions?

Example:
x/2 + y/8 = 4
x/3 - y/2 = -2

Solving systems of linear equations involving decimals and fractions

  1. Scale the system so that integer coefficients exist.
  2. Use elimination to solve for the solutions, if they exist.

Examples:
System 1
0.05x - 0.03y = 0.21
0.07x + 0.02y = 0.16

System 2
x/4 + y/6 = 1
x - y = 3

System 3
(x + 3)/4 + (y - 1)/3 = 1
2x - y = 1

Solving System Of Linear Equations by Adding (with decimals)

Examples:
3.5x + 2.5y = 17
-1.5x - 7.5y = -33

Solving Systems of Linear Equations with Fractions

Solve a system of linear equations using multiplication with addition or subtraction.

Examples:
x/2 + y/3 = -4
x/5 + y/5 = -2



Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

Fraction Concoction Game



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