Intersections of Linear Equations

Hadyn and Alex are planning to meet at a park which is at the intersection of two streets represented by two equations. What is the first step they should take to find the park by graphing these equations?

• Substitute one street's equation into the other.

• Solve one of the street's equation for a variable.

• Find the slope of each street's equation.

• Plot the streets' equations on the same coordinate plane.

Alex, Dyron, and Jake are running a lemonade stand. They are trying to figure out the sales of their two different lemonade recipes. If the graphs of these sales equations intersect at a single point, how many solutions does this system of equations have?

• 2

• 1

• 3

• 0

Diego and Miles Morales are planning their monthly budget. They each have a system of equations representing their monthly expenses. What does the intersection point of their expense graphs represent?

• The intersection point represents the sum of their expenses.

• The intersection point represents the average of their expenses.

• The intersection point represents the solution to the system of equations.

• The intersection point represents the maximum of their expenses.

Batman and Alex are trying to solve a system of equations representing the sales of two different types of ice cream in their school canteen. They found that the intersection point of the two graphs is (-2, 3). What does this mean in terms of the system of equations?

• The system of equations has a solution of x = -2 and y = 3.

• The system of equations has a solution of x = 3 and y = -2

• The system of equations has no solution, meaning that there is no price at which both types of ice cream sell the same number of units.

• The system of equations has infinitely many solutions, meaning that there are infinite prices at which both types of ice cream sell the same number of units.

Corey and Scott are trying to solve a system of equations to find out how many baseballs and footballs they have in total. Their graphs intersect at exactly one point. What is the maximum number of solutions they can obtain from their system of equations?

• Two

• Infinite

• One

• None

Diego and Alex are running two different lemonade stands. They are trying to solve a system of equations representing the sales of lemonade at their respective stands. If the graphs of these equations do not intersect, what does it mean?

• The system of equations has infinitely many solutions, meaning both lemonade stands have the same sales.

• The system of equations has one solution, meaning there is a point where both lemonade stands have the same sales.

• The system of equations has no solution, meaning there is no point where both lemonade stands have the same sales.

• The solution to the system of equations is a complex number, meaning the sales of the lemonade stands cannot be compared directly.

Peter Parker, Artie, Dustin, Diego, and Tyson are working on a project to determine the location of a hidden treasure based on a set of coordinates. How can they determine if these coordinates are a solution to their system of equations?

• They can graph the coordinates and see if they lie on the lines represented by the equations.

• They can solve the equations algebraically and check if the coordinates satisfy the solutions.

• They can calculate the slopes of the lines represented by the equations and check if they match the slopes of the coordinates.

• They can substitute the values of the coordinates into the equations and check if the equations are satisfied.

Dyron and Spiderman are trying to solve a system of equations for their math homework. They notice that the graphs of their two equations are on top of each other when they plot them on their graphing calculators. In this scenario, how many solutions does this system of equations have?

• No solution

• One solution

• Two solutions

• Infinitely many

Peter Parker and Scott are trying to solve a problem. They came up with different solutions. Which one is correct? 

• Peter's solution: (1, 5)

• Scott's solution: (-2, 3)

• Both are wrong: (1, -1)

Diego, Artie, Peter Parker, Charlie, and Ghost Face are trying to solve a system of equations. How many solutions will their system have?

• No Solution

• Infinitely Many Solutions

• No Clue

• One solution