Systems of Equations

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.

Front

How do you represent a linear equation in slope-intercept form?

Back

A linear equation in slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope represents the rate of change. For example, in a savings account, it shows how much money is deposited each month.

Front

What is the y-intercept in the context of a savings account?

Back

The y-intercept represents the initial amount of money in the account before any deposits are made.

Front

Write the equation for Leo's savings account after x months.

Back

y = 525x + 450

Front

Write the equation for Gladys's savings account after x months.

Back

y = 315x + 670

Front

How do you find the point where two lines intersect?

Back

To find the intersection, set the equations equal to each other and solve for the variable.

Front

If Leo saves $525 each month, how much will he have saved after 5 months?

Back

Leo will have saved $3075 after 5 months.

Front

If Gladys saves $315 each month, how much will she have saved after 5 months?

Back

Gladys will have saved $2245 after 5 months.

Front

What is the solution to the system of equations for Leo and Gladys's savings?

Back

The solution is the point where their savings are equal, which occurs after 2 months with $1300 each.