System of Equations Word Problems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

What does it mean if a system of equations has a unique solution?

Back

The two lines represented by the equations intersect at exactly one point.

Front

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

Back

The two 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

The two lines represented by the equations are the same line.

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, 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

If x + y = 10 and x - y = 2, what is the solution?

Back

(6, 4)

Front

If a system of equations is represented by y = 2x + 3 and y = -x + 1, what is the solution?

Back

(−2, −1)

Front

In the context of word problems, what does 'x' typically represent?

Back

A variable representing an unknown quantity that needs to be determined.