QuestionPart 1 of 6
Let $x$ represent the length of the rectangle. Let $y$ represent the width of the rectangle. The statement of the problem gives two independent relationships between the length and the width of the rectangle. The perimeter of the rectangle is 42 cm . $2 x+2 y=42$
The area is $98 \mathrm{~cm}^{2}$ . $x y=98$
Part 2 of 6
Using the substitution method, solve for $x$ or $y$ in either equation. (A) $2 x+2 y=42$
B $x y=98$
Solve for $y$ . $\qquad$ $y=21-x$
Correct Answer: $y=\frac{98}{x}$
Part: $2 / 6$
Part 3 of 6
Substitute $y=\frac{98}{x}$ from equation $B$ into equation $A$ . (A) $2 x+2\left(\frac{98}{x}\right)=42$ . $2 x+\square=42$

Studdy Solution

STEP 1

1. We have two equations representing the perimeter and area of a rectangle.
2. We are using the substitution method to solve for one variable in terms of the other.
3. We need to substitute the expression for $y$ from equation $B$ into equation $A$ .

STEP 2

1. Solve for $y$ in terms of $x$ using equation $B$ .
2. Substitute the expression for $y$ into equation $A$ .
3. Simplify the resulting equation.

STEP 3

We are given the equation for the area of the rectangle:
$x y = 98$
We solve for $y$ in terms of $x$ :
$y = \frac{98}{x}$

STEP 4

Substitute $y = \frac{98}{x}$ into the perimeter equation $A$ :
$2x + 2y = 42$
Substitute the expression for $y$ :
$2x + 2\left(\frac{98}{x}\right) = 42$

STEP 5

Simplify the equation by distributing the 2:
$2x + \frac{196}{x} = 42$
The equation $2x + \frac{196}{x} = 42$ is the result of substituting $y = \frac{98}{x}$ into equation $A$ .

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