Systems of equation 12/18

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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

What does it mean if a system of equations has no solution?

Back

It means the equations represent parallel lines that 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

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

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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

Front

What is the point of intersection of two lines?

Back

It is the solution to the system of equations represented by those lines.

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the values back into the original equations to see if they hold true.