Question Solve the linear equation $-16y = -32$ to find the value of $y$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a linear equation in one variable, $y$ .
2. We need to solve for $y$ by simplifying the equation and isolating $y$ on one side.

STEP 2

First, we need to distribute the $-8$ across the terms inside the parentheses.
$-8(2y - 2) + 17 = 1$

STEP 3

Apply the distributive property.
$-8 \cdot 2y + (-8) \cdot (-2) + 17 = 1$

STEP 4

Perform the multiplication.
$-16y + 16 + 17 = 1$

STEP 5

Combine the like terms on the left side of the equation, which are the constant terms $16$ and $17$ .
$-16y + (16 + 17) = 1$

STEP 6

Add the constant terms together.
$-16y + 33 = 1$

STEP 7

To isolate the term with $y$ , we need to move the constant term on the left side to the right side of the equation. We do this by subtracting $33$ from both sides.
$-16y + 33 - 33 = 1 - 33$

STEP 8

Simplify both sides of the equation.
$-16y = -32$

STEP 9

Now, we need to solve for $y$ by dividing both sides of the equation by $-16$ .
$\frac{-16y}{-16} = \frac{-32}{-16}$

STEP 10

Perform the division.
$y = 2$
The solution to the equation is $y = 2$ .

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