Solve Systems of Equations by Substitution

Front

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.

Front

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

Back

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

Front

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

Back

Get either variable by itself.

Front

If you have the equations y = 2x + 1 and y = 4x - 1, how do you find the solution?

Back

Set 2x + 1 equal to 4x - 1 and solve for x. Then substitute x back to find y.

Front

What is the solution to the system of equations x - 3y = -13 and 4x + 2y = 4?

Back

(-1, 4)

Front

What does it mean if two lines in a system of equations do not intersect?

Back

It means the system has no solution.

Front

What does it mean if two lines in a system of equations are the same line?

Back

It means the system has an infinite number of solutions.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the solution to the system of equations y = 8 and y = -4x + 4?

Back

(-1, 8)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines representing the equations.