Applications Solving Systems of Equations

How many solutions does this system have?

y = -5x -1

y = -5x +7

• No solutions

• One solution

• Two solutions

• Infinite solutions

What could be the first step in solving the system? CHOOSE TWO!

-10x + 3y = 5

x = y - 4

• Substitute y - 4 into the first equation for y

• Substitute y - 4 into the first equation for x

• Rewrite the second equation in standard form then multiply it by -3 to eliminate y

• Rewrite the second equation in standard form then multiply it by 3 to eliminate y

Is (5, 2) a solution to the system?

-x + 4y = 4

-x + 3y = 1

• No, it satisfies the first but not the second

• No, it satisfies the second but not the first

• No, it satisfies neither equation

• Yes, it satisfies both equations

How many solutions does

this system have?

5y = 15x - 40

y = 3x - 8

• No solutions

• One solution

• Two solutions

• Infinite solutions

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

What is the purpose of using systems of equations in real-world problems?

• To find the slope of a line

• To graph equations in a digital environment

• To solve problems with multiple variables and constraints

• To find the y-intercept

Which of the following is a real-world example of a system of equations?

• Finding the area of a rectangle

• Determining the cost of two items with different prices

• Solving for one unknown variable

• Calculating the exact speed of a car

Anna buys pens for $2 and pencils for $5. She buys 7 items and spends $26. Which system of equations represents this?

A restaurant sells steak meals for $20 and chicken meals for $15. If 30 meals total $500, what system represents this?

100 tickets sold. Adult tickets are $10, and student tickets are $5. Total revenue is $700. What are the equations?