Algebra Systems of Equations Practice

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

Back

It means there are no values for the variables that can satisfy all equations in the system.

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What does it mean for a system of equations to have infinite solutions?

Back

It means there are an unlimited number of values for the variables that satisfy all equations in the system.

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How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Add or subtract the equations to eliminate one variable. 3. Solve for the remaining variable.

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What is the graphical representation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

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What is the solution to the system: y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The point where the two lines intersect.

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What is the solution to the system: 3x + 2y = 6 and 6x + 4y = 12?

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Infinite solutions - The second equation is a multiple of the first.

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What is the solution to the system: x + y = 5 and x - y = 1?

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(3, 2) - The point where the two lines intersect.