System of Equations Review

Front

What is a system of equations?

Back

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 to solve a system of equations by elimination?

Back

It involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other variable.

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28

Back

(7, 0)

Front

What is the solution to the system: x - y = 6 and y = 2x - 5?

Back

(-1, -7)

Front

David sells nachos for $1.50 and sodas for $0.50. He made $78.50 from selling 87 items. Write the system of equations for this situation.

Back

1.5x + 0.5y = 78.5 and x + y = 87

Front

What is the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

Back

1

Front

Solve by elimination: -2x + 6y = 16 and -4x - 3y = 2

Back

(-2, 2)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.