Solving Systems 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.

Front

What does it mean to solve a system of equations?

Back

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

Front

What is substitution in solving equations?

Back

Substitution is replacing one variable with an expression that contains another variable.

Front

If y = 2x + 3, what is y when x = 1?

Back

y = 5.

Front

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

Back

Solve one of the equations for one variable.

Front

What does it mean if two lines intersect at a point?

Back

It means there is one unique solution to the system of equations.

Front

What is the solution to the system: y = 3x + 1 and y = 2x + 4?

Back

x = 3, y = 10.

Front

What happens if the lines are parallel?

Back

If the lines are parallel, there is no solution to the system.

Front

What is the solution to the system: x + y = 5 and x - y = 1?

Back

x = 3, y = 2.

Front

What does it mean if the system has infinitely many solutions?

Back

It means the equations represent the same line.