Systems of Equations-PRE TEST

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 by elimination?

Back

You manipulate the equations to eliminate one variable, allowing you to solve for the other.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A method for solving systems of equations where one equation is solved for one variable and substituted into the other.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and finding the point(s) where they intersect.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

It means they have the same slope but different y-intercepts, resulting in no points of intersection.

Front

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

Back

No solution (the lines are parallel).

Front

What is the solution to the system: 5x + 8y = -12 and 3x + 5y = -7?

Back

(-4, 1).