Solve Systems 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.

Front

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

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

Set the two equations equal to each other: 2x + 1 = 4x - 1.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

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.

Front

What is the solution to the system: 3x + y = 1 and y = 4x + 1?

Back

(0, 1)

Front

How do 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: 6x + y = -1 and y = -3x - 4?

Back

(1, -7)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Front

What is the solution to the system: y = -2x + 5 and y = 2x - 11?

Back

(4, -3)