Substitution Basics

Front

What is a solution to a system of equations?

Back

A point \( (x,y) \) where the equations intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you know when a system is ready for substitution?

Back

When \( x \) and/or \( y \) is isolated in at least one equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have 'infinitely many solutions'?

Back

The lines representing the equations are the same line, overlapping completely.

Tags

CCSS.8.EE.C.8A

Front

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

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

If \( -y = 8 \), how do you isolate \( y \)?

Back

Divide both sides by -1 to get \( y = -8 \).

Tags

CCSS.6.EE.B.7

Front

What is the substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the general form of a linear equation?

Back

The form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does it mean for a variable to be 'isolated' in an equation?

Back

It means the variable is alone on one side of the equation.

Tags

CCSS.7.EE.B.4A

Front

How can you tell if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A