System 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 solution to a system of equations?

Back

A solution is a set of values for the variables that makes all equations true.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect at a point?

Back

The point of intersection is the unique solution to the system of equations.

Front

What does it mean if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines are coincident?

Back

The system has infinitely many solutions because the lines overlap.

Front

How do you solve a system of equations by 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 by elimination?

Back

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

Front

What is the solution to the system: y = 2x + 3 and y = -x + 1?

Back

(−2, −1) is the solution.