Solving Systems by Graphing and Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for two lines to intersect?

Back

Two lines intersect when they have a common point, meaning they share the same x and y coordinates at that point.

Tags

CCSS.HSG.CO.A.1

Front

How do you solve a system of equations by graphing?

Back

To solve a system of equations by graphing, plot both equations on the same coordinate plane and identify the point where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line 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 slope of a line given two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinates (0, b) in the equation y = mx + b.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Tags

CCSS.8.EE.B.6

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Tags

CCSS.8.EE.B.6

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted into them.