Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line, coinciding with each other.

Front

How do you solve a system of equations using the substitution method?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using the elimination method?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the lines intersect.

Front

If the equations are y = 2x + 1 and y = 4x - 1, what is the solution?

Back

(1, 3) - The lines intersect at this point.

Front

What do parallel lines indicate in a system of equations?

Back

They indicate that there is no solution to the system.

Front

What is the solution to the system 3x - 2y = 14 and 2x + 2y = 6?

Back

(4, -1) - The lines intersect at this point.