Solved on Dec 04, 2023

Find the values of $x$ and $y$ that satisfy the equation $12x - 10y = 18$ . Reduce all fractions to lowest terms.

STEP 1

Assumptions
1. The given equation is $12x - 10y = 18$ .
2. We need to find the values of $x$ and $y$ that satisfy the equation.
3. If multiple solutions exist, we only need to identify one.

STEP 2

We can start by finding a value for $x$ when $y = 0$ .
To do this, we substitute $y = 0$ into the equation and solve for $x$ .
$12x - 10(0) = 18$

STEP 3

Simplify the equation by removing the term with zero.
$12x = 18$

STEP 4

Solve for $x$ by dividing both sides of the equation by 12.
$x = \frac{18}{12}$

STEP 5

Reduce the fraction to its lowest terms.
$x = \frac{3}{2}$

STEP 6

Now, we can find a value for $y$ when $x = 0$ .
To do this, we substitute $x = 0$ into the equation and solve for $y$ .
$12(0) - 10y = 18$

STEP 7

Simplify the equation by removing the term with zero.
$-10y = 18$

STEP 8

Solve for $y$ by dividing both sides of the equation by -10.
$y = \frac{18}{-10}$

STEP 9

Reduce the fraction to its lowest terms.
$y = -\frac{9}{5}$
So, the values of the missing entries are $x = \frac{3}{2}$ and $y = -\frac{9}{5}$ .

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Find the values of $x$ and $y$ that satisfy the equation $12x - 10y = 18$ . Reduce all fractions to lowest terms.

STEP 1

Assumptions
1. The given equation is $12x - 10y = 18$ .
2. We need to find the values of $x$ and $y$ that satisfy the equation.
3. If multiple solutions exist, we only need to identify one.

STEP 2

We can start by finding a value for $x$ when $y = 0$ .
To do this, we substitute $y = 0$ into the equation and solve for $x$ .
$12x - 10(0) = 18$

STEP 3

Simplify the equation by removing the term with zero.
$12x = 18$

STEP 4

Solve for $x$ by dividing both sides of the equation by 12.
$x = \frac{18}{12}$

STEP 5

Reduce the fraction to its lowest terms.
$x = \frac{3}{2}$

STEP 6

Now, we can find a value for $y$ when $x = 0$ .
To do this, we substitute $x = 0$ into the equation and solve for $y$ .
$12(0) - 10y = 18$

STEP 7

Simplify the equation by removing the term with zero.
$-10y = 18$

STEP 8

Solve for $y$ by dividing both sides of the equation by -10.
$y = \frac{18}{-10}$

STEP 9

Reduce the fraction to its lowest terms.
$y = -\frac{9}{5}$
So, the values of the missing entries are $x = \frac{3}{2}$ and $y = -\frac{9}{5}$ .

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Find the values of xxx and yyy that satisfy the equation 12x−10y=1812x - 10y = 1812x−10y=18. Reduce all fractions to lowest terms.

STEP 1

Assumptions1. The given equation is 12x−10y=1812x - 10y = 1812x−10y=18.2. We need to find the values of xxx and yyy that satisfy the equation.3. If multiple solutions exist, we only need to identify one.

STEP 2

We can start by finding a value for xxx when y=0y = 0y=0. To do this, we substitute y=0y = 0y=0 into the equation and solve for xxx.12x−10(0)=1812x - 10(0) = 1812x−10(0)=18

STEP 3

Simplify the equation by removing the term with zero.12x=1812x = 1812x=18

STEP 4

Solve for xxx by dividing both sides of the equation by 12.x=1812x = \frac{18}{12}x=1218​

STEP 5

Reduce the fraction to its lowest terms.x=32x = \frac{3}{2}x=23​

STEP 6

Now, we can find a value for yyy when x=0x = 0x=0. To do this, we substitute x=0x = 0x=0 into the equation and solve for yyy.12(0)−10y=1812(0) - 10y = 1812(0)−10y=18

STEP 7

Simplify the equation by removing the term with zero.−10y=18-10y = 18−10y=18

STEP 8

Solve for yyy by dividing both sides of the equation by -10.y=18−10y = \frac{18}{-10}y=−1018​

STEP 9

Reduce the fraction to its lowest terms.y=−95y = -\frac{9}{5}y=−59​So, the values of the missing entries are x=32x = \frac{3}{2}x=23​ and y=−95y = -\frac{9}{5}y=−59​.

Start learning now

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

Find the values of $x$ and $y$ that satisfy the equation $12x - 10y = 18$ . Reduce all fractions to lowest terms.

Assumptions
1. The given equation is $12x - 10y = 18$ .
2. We need to find the values of $x$ and $y$ that satisfy the equation.
3. If multiple solutions exist, we only need to identify one.

We can start by finding a value for $x$ when $y = 0$ .
To do this, we substitute $y = 0$ into the equation and solve for $x$ .
$12x - 10(0) = 18$

Simplify the equation by removing the term with zero.
$12x = 18$

Solve for $x$ by dividing both sides of the equation by 12.
$x = \frac{18}{12}$

Reduce the fraction to its lowest terms.
$x = \frac{3}{2}$

Now, we can find a value for $y$ when $x = 0$ .
To do this, we substitute $x = 0$ into the equation and solve for $y$ .
$12(0) - 10y = 18$

Simplify the equation by removing the term with zero.
$-10y = 18$

Solve for $y$ by dividing both sides of the equation by -10.
$y = \frac{18}{-10}$

Reduce the fraction to its lowest terms.
$y = -\frac{9}{5}$
So, the values of the missing entries are $x = \frac{3}{2}$ and $y = -\frac{9}{5}$ .