Solving Systems 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 system of equations to have a unique solution?

Back

It means that the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so they intersect at every point on that 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, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

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

Back

1

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

What is the solution of the two linear equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)