Systems of Linear Equations Review

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphing method?

Back

A method of solving systems of equations by graphing the equations on the same coordinate plane and identifying the intersection point.

Tags

CCSS.8.EE.C.8B

Front

What is the equal values method?

Back

A method where two equations are set equal to each other to find the variable values.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, every point on the line is a solution, indicating infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations: x + 2y = -3 and x - y = -12?

Back

(-9, 3) is the solution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations: 5x + 3y = 8 and 3x - 3y = 0?

Back

(1, 1) is the solution.

Tags

CCSS.HSA.REI.C.9