Unit 4 Review: Solving Systems of Equations

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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

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

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply if necessary to get coefficients to match. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Front

What is the solution to the system of equations y = 2x - 11 and -3y = -6x - 15?

Back

No solution (the lines are parallel).

Front

What is the solution to the system of equations 8x + 4y = 12 and y = -2x + 3?

Back

Infinitely many solutions (the lines are the same).

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3).

Front

What is the solution to the system of equations 5x + 3y = 7 and y = 4?

Back

(-1, 4).