A.2I & A.3D Practice

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 the cost of a pizza with toppings as a linear equation?

Back

If a pizza costs $6.80 and each topping costs $0.90, the equation is: y = 6.80 + 0.90x, where y is the total cost and x is the number of toppings.

Front

What is the purpose of solving a system of equations?

Back

The purpose is to find the values of the variables that satisfy all equations in the system simultaneously.

Front

How can you represent Nancy's grocery purchases with equations?

Back

Let x be the price of an apple and y be the price of a banana. The equations are: 4x + 6y = 13 (Monday) and 3x + 7y = 13.5 (Wednesday).

Front

What does it mean for two lines to intersect in a system of equations?

Back

It means that there is a common solution for the variables, which is the point where the two lines meet on a graph.

Front

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

Back

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

Front

How do you find the slope of a line given two points?

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.