Writing Systems of Equations Through Word Problems

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

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

Tags

CCSS.HSA.CED.A.3

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the two equations have a common solution, which is the point where both equations are true.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the point (3, 19) in the context of the problem?

Back

It represents the number of items sold by both Lisa and Tammy when they have earned the same amount.

Tags

CCSS.8.EE.C.8C

Front

How can you determine the solution to a system of equations graphically?

Back

By plotting both equations on the same graph and identifying the point where they intersect.

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

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change, such as how many items are sold per hour.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How do you find the solution to a system of equations algebraically?

Back

You can use methods such as substitution, elimination, or matrix operations to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a word problem?

Back

A word problem is a mathematical problem presented in the form of a narrative, requiring interpretation and translation into equations.

Tags

CCSS.8.EE.C.7B