Consider the equation 2x + 2y = 8.
part a: write an equivalent equation by multiplying the equation by 3.
does the equation have the same solution set?
part b: write an equivalent equation by dividing the equation by 2. does
the equation have the same solution set?

Part A) see the explanation

Part B) see the explanation

Step-by-step explanation:

we have

Part A) Write an equivalent equation by multiplying the equation by 3.

Does the equation have the same solution set?

Multiply by 3 both sides

Remember that

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal

therefore

The equivalent equation have the same solution set by multiplication property of equality

Part B) Write an equivalent equation by dividing the equation by 2. Does

the equation have the same solution set?

Divide by 2 both sides

Remember that

The Division Property of Equality states that if you divide both sides of an equation by the same number, the sides remain equal

therefore

The equivalent equation have the same solution set by division property of equality

Number of Small Cones Sold=22

Number of Large Cones Sold=34

Step-by-step explanation:

Suppose,

Number of Small Cones Sold: s

Number of Large Cones Sold: l

For the condition that, larges cones sold were 12 more than small ones, equation would be

and for the total revenue condition of $163

By solving equation (i) and (ii) simultaneously, we get

s=22

and

l=34

Hence, small cones sold would be 22 and large cones sold would be 34.