Solving Systems of Equations using Elimination

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations true, resulting in one x value and one y value that satisfy both equations.

Front

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

Back

It means there is exactly one pair of values (x, y) that satisfies both equations.

Front

How do you determine the cost of one shirt if the younger brother spent $175 on 7 shirts and 7 shorts, and the older brother spent $165 on 6 shirts and 7 shorts?

Back

The cost of one shirt is $10.

Front

What system of equations represents two running backs who rushed a combined total of 1550 yards, with one rushing 4 times as many yards as the other?

Back

The system of equations is: x + y = 1550 and y = 4x.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of 2 or more equations that share the same variables.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that 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 elimination?

Back

You eliminate one variable by adding or subtracting the equations to find the value of the other variable.

Front

What is the first step in solving the system 7x + 2y = 24 and 8x + 2y = 30 using elimination?

Back

Subtract the first equation from the second to eliminate y.

Front

What is the solution to the system 7x + 2y = 24 and 8x + 2y = 30?

Back

The solution is (6, -9).