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 simultaneously.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

What is the graphical representation of a system of equations?

Back

The solutions can be represented as the intersection points of the lines on a graph.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

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 is elimination in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

Solve the system: y = 8x + 9 and 2x + 6y = 8.

Back

(-1, 1)

Front

Solve the system: y = 8x + 1 and y = 6x + 3.

Back

(1, 9)

Front

Solve the system: y = -5x and x + 3y = 28.

Back

(-2, 10)

Front

Solve the system: -6x + 4y = 12 and y = 6.

Back

(2, 6)