Question

Write a system of equations and name their solution

Answer 1

Answer:

1. Theresa and Kayla will each sell 24 tubs of cookie dough.
2. System of equations: y = 3x + 12 and y = 6x.
3. Solution: (4, 24)

Step-by-step explanation:

Theresa's sold cookie dough can be represented by the equation: 12 + 3x = y

• I started Theresa with 12 tubs of cookie dough, which is what the constant 12 shows.
• Days are represented by the variable x, and 3x represents Theresa's selling of 3 tubs a day.
• All of these terms are equal to the variable y which represents the total number of tubs sold.

Kayla's sold cookie dough can be represented by the equation: 6x = y

• Kayla starts with no already sold tubs of cookie dough.
• The 6x represents Kayla's selling of 6 tubs a day (x). 6x is equal to y because this represents the total number of tubs sold.

They will eventually sell the same amount of cookie dough, so to find the number of tubs they each will sell to reach this equivalent amount you would make both equations equal to each other.

• 12 + 3x = 6x
• Subtract 3x from both sides of the equation.
• 12 = 3x
• Divide both sides of the equation by 3.
• x = 4

To find the number of tubs they each sell, substitute 4 for x into each of their respective equations.

• Theresa:  $12+3x\rightarrow12+3(4)\rightarrow 12 + 12 = 24$
• Kayla:  $6x\rightarrow 6(4)=24$
• They both sell the same amount of tubs so it makes sense that they both sell 24.

By substituting in x, we found y. This means that the solution to the system of equations is (x, y) ⇒ (4, 24).

To graph these equations:

Theresa: y = 3x + 12

• Look at the constant term. This represents the y-intercept; the y-intercept of this line is (0, 12). Place a point there.
• Look at the coefficient of x. This represents the slope; the slope of this line is 3(/1). This means that from the y-intercept, you will go up 3 units and to the right 1 unit.
• This line is represented by the RED LINE.

Kayla: y = 6x

• There is no constant term so the y-intercept will be at (0, 0).
• The slope of this line is 6, which means you will go up from (0, 0) 6 units and to the right 1 unit.
• This line is represented by the BLUE LINE.

On the graph (credit to desmos), you can see that they intersect at (4, 24), which is the same solution we found without graphing and by using algebra.