System of Equations Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for two equations to intersect?

Back

When two equations intersect, it means they have at least one solution in common, represented by the coordinates (x, y) where the graphs of the equations meet.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines or curves of the equations plotted on a coordinate plane.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

The solution is the point (1, 3), where the two lines intersect.

Front

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

Back

If a system has no solution, the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

If a system has infinitely many solutions, the equations represent the same line, meaning they intersect at every point on that line.

Front

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

Back

You can check by substituting the solution back into the original equations to see if both equations are satisfied.

Front

What is the price of one pack of sugar cookies if Amy sold 10 packs for $56?

Back

The price of one pack of sugar cookies is $4.