Solving pairs of linear equations in two variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

A system of equations has one solution when the lines represented by the equations intersect at exactly one point.

Front

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

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

Front

How do you solve a system of equations by graphing?

Back

To solve by graphing, plot both equations on the same graph and identify the point(s) where they intersect.

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations y = x - 4 and y = -x + 6?

Back

(5, 1)

Front

What is the solution to the system of equations y = 2/3x - 2 and y = -x + 3?

Back

(3, 0)

Front

What is the solution to the system of equations y = -2x and y = -x + 5?

Back

(-5, 10)

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.