Solved on Jan 26, 2024

Solve the linear system $17x + 17y = 15$ for integers, proper fractions, and improper fractions.

STEP 1

Assumptions
1. We have a linear equation in two variables, $x$ and $y$ .
2. The equation is $17x + 17y = 15$ .
3. We need to express the solution in terms of $x$ or $y$ using integers, proper fractions, or improper fractions in simplest form.

STEP 2

First, we should simplify the equation by factoring out the common factor of $17$ from the left-hand side.
$17x + 17y = 17(x + y)$

STEP 3

Now, rewrite the equation using the factored form.
$17(x + y) = 15$

STEP 4

Next, we divide both sides of the equation by $17$ to isolate the term $(x + y)$ .
$\frac{17(x + y)}{17} = \frac{15}{17}$

STEP 5

Simplify both sides of the equation.
$x + y = \frac{15}{17}$

STEP 6

Now we can express $y$ in terms of $x$ or $x$ in terms of $y$ . Let's solve for $y$ in terms of $x$ .
$y = \frac{15}{17} - x$

STEP 7

We have expressed $y$ in terms of $x$ using a proper fraction. This equation represents an infinite number of solutions where $x$ and $y$ are dependent on each other.
The solution to the equation $17x + 17y = 15$ in terms of $y$ is:
$y = \frac{15}{17} - x$

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Solve the linear system $17x + 17y = 15$ for integers, proper fractions, and improper fractions.

STEP 1

Assumptions
1. We have a linear equation in two variables, $x$ and $y$ .
2. The equation is $17x + 17y = 15$ .
3. We need to express the solution in terms of $x$ or $y$ using integers, proper fractions, or improper fractions in simplest form.

STEP 2

First, we should simplify the equation by factoring out the common factor of $17$ from the left-hand side.
$17x + 17y = 17(x + y)$

STEP 3

Now, rewrite the equation using the factored form.
$17(x + y) = 15$

STEP 4

Next, we divide both sides of the equation by $17$ to isolate the term $(x + y)$ .
$\frac{17(x + y)}{17} = \frac{15}{17}$

STEP 5

Simplify both sides of the equation.
$x + y = \frac{15}{17}$

STEP 6

Now we can express $y$ in terms of $x$ or $x$ in terms of $y$ . Let's solve for $y$ in terms of $x$ .
$y = \frac{15}{17} - x$

STEP 7

We have expressed $y$ in terms of $x$ using a proper fraction. This equation represents an infinite number of solutions where $x$ and $y$ are dependent on each other.
The solution to the equation $17x + 17y = 15$ in terms of $y$ is:
$y = \frac{15}{17} - x$

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Solve the linear system 17x+17y=1517x + 17y = 1517x+17y=15 for integers, proper fractions, and improper fractions.

STEP 1

Assumptions1. We have a linear equation in two variables, xxx and yyy.2. The equation is 17x+17y=1517x + 17y = 1517x+17y=15.3. We need to express the solution in terms of xxx or yyy using integers, proper fractions, or improper fractions in simplest form.

STEP 2

First, we should simplify the equation by factoring out the common factor of 171717 from the left-hand side.17x+17y=17(x+y)17x + 17y = 17(x + y)17x+17y=17(x+y)

STEP 3

Now, rewrite the equation using the factored form.17(x+y)=1517(x + y) = 1517(x+y)=15

STEP 4

Next, we divide both sides of the equation by 171717 to isolate the term (x+y)(x + y)(x+y).17(x+y)17=1517\frac{17(x + y)}{17} = \frac{15}{17}1717(x+y)​=1715​

STEP 5

Simplify both sides of the equation.x+y=1517x + y = \frac{15}{17}x+y=1715​

STEP 6

Now we can express yyy in terms of xxx or xxx in terms of yyy. Let's solve for yyy in terms of xxx.y=1517−xy = \frac{15}{17} - xy=1715​−x

STEP 7

We have expressed yyy in terms of xxx using a proper fraction. This equation represents an infinite number of solutions where xxx and yyy are dependent on each other.The solution to the equation 17x+17y=1517x + 17y = 1517x+17y=15 in terms of yyy is:y=1517−xy = \frac{15}{17} - xy=1715​−x

Start learning now

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

Solve the linear system $17x + 17y = 15$ for integers, proper fractions, and improper fractions.

Assumptions
1. We have a linear equation in two variables, $x$ and $y$ .
2. The equation is $17x + 17y = 15$ .
3. We need to express the solution in terms of $x$ or $y$ using integers, proper fractions, or improper fractions in simplest form.

First, we should simplify the equation by factoring out the common factor of $17$ from the left-hand side.
$17x + 17y = 17(x + y)$

Now, rewrite the equation using the factored form.
$17(x + y) = 15$

Next, we divide both sides of the equation by $17$ to isolate the term $(x + y)$ .
$\frac{17(x + y)}{17} = \frac{15}{17}$

Simplify both sides of the equation.
$x + y = \frac{15}{17}$

Now we can express $y$ in terms of $x$ or $x$ in terms of $y$ . Let's solve for $y$ in terms of $x$ .
$y = \frac{15}{17} - x$

We have expressed $y$ in terms of $x$ using a proper fraction. This equation represents an infinite number of solutions where $x$ and $y$ are dependent on each other.
The solution to the equation $17x + 17y = 15$ in terms of $y$ is:
$y = \frac{15}{17} - x$