Solving Systems by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and then drawing a line through those points.

Front

What is the solution to a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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 every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions by graphing?

Back

By graphing the equations and observing the intersection: one point (one solution), parallel lines (no solution), or the same line (infinitely many solutions).

Tags

CCSS.8.EE.C.8B

Front

Solve the system by graphing: y = 2x + 1 and y = -x + 4.

Back

The solution is (1, 3).

Tags

CCSS.8.EE.C.8B

Front

Solve the system by graphing: 3x + 2y = 6 and x - y = 1.

Back

The solution is (2, 0).

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.