Systems of Equations - 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?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What does it mean if a system of equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect, meaning there are no common solutions.

Front

Solve the system of equations: y = -2x + 1 and y = 1 - 2x.

Back

Infinite solutions.

Front

Solve the system of equations: y = 2x + 1 and y = 2x - 7.

Back

No solution.

Front

Solve the system of equations: y = 2x - 8 and 3y + 2x = 16.

Back

(5, 2).

Front

Solve for x and y using substitution: y = 2x + 1 and y = -3x + 1.

Back

(0, 1).

Front

Solve the system of equations: x = 7 - 3y and 2x - 3y = -4.

Back

(1, 2).