How to Solve Special Systems in Algebra

Special systems have no solution or an infinite number of solutions.
••• Pixland/Pixland/Getty Images

A special system consists of two linear equations that are parallel or have an infinite number of solutions.To solve these equations, you add or subtract them and solve for the variables x and y. Special systems may seem challenging at first, but once you practice these steps, you'll be able to solve or graph any similar type of problem.

No Solution

    Write the special system of equations in a stack format. For example: x+y=3 y= -x-1.

    Rewrite so the equations are stacked above their corresponding variables.

    y= -x +3 y= -x-1

    Eliminate the variable(s) by subtracting the bottom equation from the top equation. The result is: 0=0+4. 0≠4. Therefore, this system has no solution. If you graph the equations on paper, you will see that the equations are parallel lines and do not intersect.

Infinite Solution

    Write the system of equations in a stack format. For example: -9x -3y= -18 3x+y=6

    Multiply the bottom equation by 3: \=3(3x+y)=3(6) \=9x+3y=18

    Rewrite the equations in stacked format: -9x -3y= -18 9x+3y=18

    Add the equations together. The result is: 0=0, which means that both equations are equal to the same line, thus there are infinite solutions. Test this by graphing both equations.

Related Articles

How to Solve Linear Equations With 2 Variables
3 Methods for Solving Systems of Equations
How to Solve a Parabola
Equation for Curved Lines in Algebra
How to Find Asymptotes & Holes
Algebra 1 Substitution Method
How to Draw an Array in Math
How to Find X & Y Intercepts on a Graphing Calculator
How to Figure Out the Slope of a Line
The Difference Between Linear & Nonlinear Equations
How to Convert Graphs to Equations
How to Find the Slope of a Plotted Line With the TI-84...
What Is the Difference Between a Quadratic and a Linear...
Algebra 1 Compared to Algebra 2
How to Teach Multiplication to the Second Grade Using...
Infinite Solution Elimination Method
How to Calculate Correlation
Difference Between Linear Equations & Linear Inequalities
How to Use Elimination to Solve the Linear Equation
How to Find the X Intercept of a Function