Solving systems of equations 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?

Back

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

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

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

Back

(1, 3)

Front

Solve the system: y = -2x + 5 and y = 2x - 11.

Back

(4, -3)

Front

Solve the system: 3x + 2y = 8 and -x + y = -11.

Back

(6, -5)