Solving Systems Using Substitution and Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does substitution mean in solving systems of equations?

Back

Substitution 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 does elimination mean in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is substitution the preferred method?

Back

Substitution is preferred when one equation is easily solvable for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

When is elimination the preferred method?

Back

Elimination is preferred when the coefficients of one variable are easily manipulated to cancel out.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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. 4. Substitute back to find the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get equal coefficients. 3. Add or subtract the equations to eliminate one variable. 4. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to a system of equations?

Back

The solution is the point (x, y) where the two equations intersect, representing the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and there are countless points of intersection.

Tags

CCSS.8.EE.C.8A