Solving 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 of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

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.

Front

What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the lines representing the equations intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution, as the lines never intersect.

Front

What is the solution to the system of equations: y = -2x + 18 and y = 8?

Back

(5, 8)

Front

What is the substitution method used for?

Back

To find the values of variables that satisfy all equations in a system.