Systems of Equations

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What is a system of equations?

Back

A system of equations is a set of two or more 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 equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

What is the first step in solving a system of equations using substitution?

Back

The first step is to isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 8 + 3 = 11.

Tags

CCSS.HSF.IF.A.2

Front

What is the elimination method used for?

Back

The elimination method is used to eliminate one variable by adding or subtracting equations, simplifying the system to one equation with one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6