Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

Front

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

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Tags

CCSS.7.EE.B.4A

Front

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

Back

Choose one equation and solve for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations x = 7 - 2y and 2x + y = 5, what is the value of y when x = 1?

Back

y = 3.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection of the lines representing each equation on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you find the solution?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6