Solve Systems by Graphing and Substitution

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

Front

How do you solve a system of equations by graphing?

Back

Plot both equations on the same graph and identify the point(s) where they intersect.

Front

What does it mean for a point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Front

What is substitution in solving systems of equations?

Back

Substitution involves solving one equation for a variable and then substituting that expression into another equation.

Front

Solve by substitution: y = 2x + 3, x = 1.

Back

(1, 5)

Front

Solve by graphing: y = x + 2, y = -x + 4.

Back

(2, 3)

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

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

Back

Substitute the point's coordinates into each equation to see if they hold true.

Front

Solve by substitution: 3x + 2y = 12, y = 2.

Back

(2, 2)

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.