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 represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can you find the point of intersection of two lines represented by equations?

Back

To find the point of intersection, solve the system of equations simultaneously to find the values of x and y that satisfy both equations.

Front

What is the initial amount in Leo's savings account?

Back

The initial amount in Leo's savings account is $450.

Front

What is the monthly deposit amount for Gladys?

Back

Gladys deposits $635 each month into her savings account.

Front

How do you set up a system of equations for savings accounts?

Back

Let x be the number of months. For Leo: y = 662.50x + 450; For Gladys: y = 635x + 670.

Front

How do you calculate the total savings after a certain number of months?

Back

Total savings can be calculated using the equation: Total Savings = Initial Amount + (Monthly Deposit × Number of Months).

Front

What is the total amount Leo will have after 8 months?

Back

After 8 months, Leo will have $5750.