Solved on Jan 21, 2024

Solve the linear equation $\frac{y}{5}-7=-2 x$ for $x$ and $y$ .

STEP 1

Assumptions
1. We are given the equation $\frac{y}{5}-7=-2x$ .
2. We need to solve for $y$ in terms of $x$ .

STEP 2

We start by isolating the term containing $y$ on one side of the equation. To do this, we add $7$ to both sides of the equation to remove the $-7$ from the left side.
$\frac{y}{5}-7+7=-2x+7$

STEP 3

Simplify both sides of the equation.
$\frac{y}{5}= -2x + 7$

STEP 4

Now, we want to solve for $y$ . To do this, we multiply both sides of the equation by $5$ to get rid of the denominator on the left side.
$5 \cdot \frac{y}{5} = 5 \cdot (-2x + 7)$

STEP 5

Simplify the left side of the equation by canceling out the $5$ in the numerator and the denominator.
$y = 5 \cdot (-2x + 7)$

STEP 6

Distribute the $5$ across the terms inside the parentheses on the right side of the equation.
$y = 5 \cdot (-2x) + 5 \cdot 7$

STEP 7

Multiply the constants.
$y = -10x + 35$
The solution to the equation $\frac{y}{5}-7=-2x$ in terms of $y$ is $y = -10x + 35$ .

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Solve the linear equation $\frac{y}{5}-7=-2 x$ for $x$ and $y$ .

STEP 1

Assumptions
1. We are given the equation $\frac{y}{5}-7=-2x$ .
2. We need to solve for $y$ in terms of $x$ .

STEP 2

We start by isolating the term containing $y$ on one side of the equation. To do this, we add $7$ to both sides of the equation to remove the $-7$ from the left side.
$\frac{y}{5}-7+7=-2x+7$

STEP 3

Simplify both sides of the equation.
$\frac{y}{5}= -2x + 7$

STEP 4

Now, we want to solve for $y$ . To do this, we multiply both sides of the equation by $5$ to get rid of the denominator on the left side.
$5 \cdot \frac{y}{5} = 5 \cdot (-2x + 7)$

STEP 5

Simplify the left side of the equation by canceling out the $5$ in the numerator and the denominator.
$y = 5 \cdot (-2x + 7)$

STEP 6

Distribute the $5$ across the terms inside the parentheses on the right side of the equation.
$y = 5 \cdot (-2x) + 5 \cdot 7$

STEP 7

Multiply the constants.
$y = -10x + 35$
The solution to the equation $\frac{y}{5}-7=-2x$ in terms of $y$ is $y = -10x + 35$ .

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Solve the linear equation y5−7=−2x\frac{y}{5}-7=-2 x5y​−7=−2x for xxx and yyy.

STEP 1

Assumptions1. We are given the equation y5−7=−2x\frac{y}{5}-7=-2x5y​−7=−2x.2. We need to solve for yyy in terms of xxx.

STEP 2

We start by isolating the term containing yyy on one side of the equation. To do this, we add 777 to both sides of the equation to remove the −7-7−7 from the left side.y5−7+7=−2x+7\frac{y}{5}-7+7=-2x+75y​−7+7=−2x+7

STEP 3

Simplify both sides of the equation.y5=−2x+7\frac{y}{5}= -2x + 75y​=−2x+7

STEP 4

Now, we want to solve for yyy. To do this, we multiply both sides of the equation by 555 to get rid of the denominator on the left side.5⋅y5=5⋅(−2x+7)5 \cdot \frac{y}{5} = 5 \cdot (-2x + 7)5⋅5y​=5⋅(−2x+7)

STEP 5

Simplify the left side of the equation by canceling out the 555 in the numerator and the denominator.y=5⋅(−2x+7)y = 5 \cdot (-2x + 7)y=5⋅(−2x+7)

STEP 6

Distribute the 555 across the terms inside the parentheses on the right side of the equation.y=5⋅(−2x)+5⋅7y = 5 \cdot (-2x) + 5 \cdot 7y=5⋅(−2x)+5⋅7

STEP 7

Multiply the constants.y=−10x+35y = -10x + 35y=−10x+35The solution to the equation y5−7=−2x\frac{y}{5}-7=-2x5y​−7=−2x in terms of yyy is y=−10x+35y = -10x + 35y=−10x+35.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the linear equation $\frac{y}{5}-7=-2 x$ for $x$ and $y$ .

Assumptions
1. We are given the equation $\frac{y}{5}-7=-2x$ .
2. We need to solve for $y$ in terms of $x$ .

We start by isolating the term containing $y$ on one side of the equation. To do this, we add $7$ to both sides of the equation to remove the $-7$ from the left side.
$\frac{y}{5}-7+7=-2x+7$

Simplify both sides of the equation.
$\frac{y}{5}= -2x + 7$

Now, we want to solve for $y$ . To do this, we multiply both sides of the equation by $5$ to get rid of the denominator on the left side.
$5 \cdot \frac{y}{5} = 5 \cdot (-2x + 7)$

Simplify the left side of the equation by canceling out the $5$ in the numerator and the denominator.
$y = 5 \cdot (-2x + 7)$

Distribute the $5$ across the terms inside the parentheses on the right side of the equation.
$y = 5 \cdot (-2x) + 5 \cdot 7$

Multiply the constants.
$y = -10x + 35$
The solution to the equation $\frac{y}{5}-7=-2x$ in terms of $y$ is $y = -10x + 35$ .