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 on a graph.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel from their equations?

Back

If their slopes are equal and their y-intercepts are different.

Front

What is the first step in solving the system: 4x - 2y = 7 and x + 2y = 3?

Back

You can use either substitution or elimination to start solving.