Solved on Jan 10, 2024

Solve the linear equation $3x + 7y = 15$ for either $x$ or $y$ .

STEP 1

Assumptions
1. We have a system of linear equations with two variables, $x$ and $y$ .
2. We are asked to isolate either $x$ or $y$ in the equation $3x + 7y = 15$ .

STEP 2

We will choose to isolate $y$ for this example. To do this, we need to move all terms involving $x$ to the other side of the equation.
$3x + 7y = 15$

STEP 3

Subtract $3x$ from both sides of the equation to move the term involving $x$ to the right side.
$3x + 7y - 3x = 15 - 3x$

STEP 4

Simplify both sides of the equation.
$7y = 15 - 3x$

STEP 5

Now, divide both sides of the equation by $7$ to isolate $y$ .
$\frac{7y}{7} = \frac{15 - 3x}{7}$

STEP 6

Simplify the equation to find the isolated $y$ .
$y = \frac{15}{7} - \frac{3x}{7}$

STEP 7

We can leave the answer in this fractional form, or we can write it as a mixed number or decimal if needed. For now, we will leave it as fractions.
So, the isolated $y$ in terms of $x$ is:
$y = \frac{15}{7} - \frac{3x}{7}$

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Solve the linear equation $3x + 7y = 15$ for either $x$ or $y$ .

STEP 1

Assumptions
1. We have a system of linear equations with two variables, $x$ and $y$ .
2. We are asked to isolate either $x$ or $y$ in the equation $3x + 7y = 15$ .

STEP 2

We will choose to isolate $y$ for this example. To do this, we need to move all terms involving $x$ to the other side of the equation.
$3x + 7y = 15$

STEP 3

Subtract $3x$ from both sides of the equation to move the term involving $x$ to the right side.
$3x + 7y - 3x = 15 - 3x$

STEP 4

Simplify both sides of the equation.
$7y = 15 - 3x$

STEP 5

Now, divide both sides of the equation by $7$ to isolate $y$ .
$\frac{7y}{7} = \frac{15 - 3x}{7}$

STEP 6

Simplify the equation to find the isolated $y$ .
$y = \frac{15}{7} - \frac{3x}{7}$

STEP 7

We can leave the answer in this fractional form, or we can write it as a mixed number or decimal if needed. For now, we will leave it as fractions.
So, the isolated $y$ in terms of $x$ is:
$y = \frac{15}{7} - \frac{3x}{7}$

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Solve the linear equation 3x+7y=153x + 7y = 153x+7y=15 for either xxx or yyy.

STEP 1

Assumptions1. We have a system of linear equations with two variables, x x x and y y y.2. We are asked to isolate either x x x or y y y in the equation 3x+7y=15 3x + 7y = 15 3x+7y=15.

STEP 2

We will choose to isolate y y y for this example. To do this, we need to move all terms involving x x x to the other side of the equation.3x+7y=153x + 7y = 153x+7y=15

STEP 3

Subtract 3x 3x 3x from both sides of the equation to move the term involving x x x to the right side.3x+7y−3x=15−3x3x + 7y - 3x = 15 - 3x3x+7y−3x=15−3x

STEP 4

Simplify both sides of the equation.7y=15−3x7y = 15 - 3x7y=15−3x

STEP 5

Now, divide both sides of the equation by 7 7 7 to isolate y y y.7y7=15−3x7\frac{7y}{7} = \frac{15 - 3x}{7}77y​=715−3x​

STEP 6

Simplify the equation to find the isolated y y y.y=157−3x7y = \frac{15}{7} - \frac{3x}{7}y=715​−73x​

STEP 7

We can leave the answer in this fractional form, or we can write it as a mixed number or decimal if needed. For now, we will leave it as fractions.So, the isolated y y y in terms of x x x is:y=157−3x7y = \frac{15}{7} - \frac{3x}{7}y=715​−73x​

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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 $3x + 7y = 15$ for either $x$ or $y$ .

Assumptions
1. We have a system of linear equations with two variables, $x$ and $y$ .
2. We are asked to isolate either $x$ or $y$ in the equation $3x + 7y = 15$ .

We will choose to isolate $y$ for this example. To do this, we need to move all terms involving $x$ to the other side of the equation.
$3x + 7y = 15$

Subtract $3x$ from both sides of the equation to move the term involving $x$ to the right side.
$3x + 7y - 3x = 15 - 3x$

Simplify both sides of the equation.
$7y = 15 - 3x$

Now, divide both sides of the equation by $7$ to isolate $y$ .
$\frac{7y}{7} = \frac{15 - 3x}{7}$

Simplify the equation to find the isolated $y$ .
$y = \frac{15}{7} - \frac{3x}{7}$

We can leave the answer in this fractional form, or we can write it as a mixed number or decimal if needed. For now, we will leave it as fractions.
So, the isolated $y$ in terms of $x$ is:
$y = \frac{15}{7} - \frac{3x}{7}$