Solve Systems by Substitution

Front

What is a system of equations?

Back

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

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 a system by substitution?

Back

Make sure at least one equation is solved for one variable.

Front

Given the equations x + y = 8 and y = x + 2, solve for x and y.

Back

x = 3, y = 5.

Front

Given the equations x - 3y = -13 and 4x + 2y = 4, solve for x and y.

Back

x = -1, y = 4.

Front

Given the equations 3x + 2y = 16 and 7x + y = 19, solve for x and y.

Back

x = 2, y = 5.

Front

Given the equations 5x + 3y = 7 and y = 4, solve for x and y.

Back

x = -1, y = 4.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the solution of a system of equations?

Back

The values of the variables that make all equations in the system true.

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.