# How to Solve Special Systems in Algebra

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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.