Solving Systems Using Substitution

Front

What is a system of equations?

Back

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

Front

What does substitution mean in solving equations?

Back

Substitution is the process of replacing a variable with an equivalent expression to solve equations.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the first step in solving the system: x = -3y - 8 and x - 2y = -3?

Back

Substitute -3y - 8 for x in the second equation.

Front

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

Back

(-1, 8) is the solution.

Front

What does it mean if two lines intersect at a point in a system of equations?

Back

It means there is one unique solution to the system.

Front

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

Back

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

Front

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

Back

It means there are infinitely many solutions, as the lines are the same.

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3) is the solution.

Front

What is the solution to the system: x = -3y - 17 and 2x + 3y = -7?

Back

(10, -9) is the solution.