QuestionSolve $3x + 6y = 24$ for $x$ and $y$ . Find both $x$ and $y$ in terms of each other.

Studdy Solution

STEP 1

Assumptions1. We are given four equations that are essentially the same, just rearranged. . We need to solve for $x$ and $y$ in terms of the other variable.
3. The equations are linear and have a unique solution.

STEP 2

Let's start by solving the first equation for $x$ .
$x +6y =24$

STEP 3

To isolate $x$ , we need to subtract $6y$ from both sides of the equation.
$3x =24 -6y$

STEP 4

Now, divide both sides by $3$ to solve for $x$ .
$x = \frac{24 -6y}{3}$

STEP 5

implify the equation for $x$ .
$x =8 -2y$

STEP 6

Now, let's solve the second equation for $y$ .
$6y =24 -3x$

STEP 7

To isolate $y$ , we need to divide both sides of the equation by $6$ .
$y = \frac{24 -3x}{6}$

STEP 8

implify the equation for $y$ .
$y =4 - \frac{1}{2}x$

STEP 9

The third and fourth equations are just rearrangements of the first two equations, so they will yield the same solutions for $x$ and $y$ .
So, the solutions are $y =4 - \frac{}{2}x$ $x =8 -2y$

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QuestionSolve $3x + 6y = 24$ for $x$ and $y$ . Find both $x$ and $y$ in terms of each other.

Studdy Solution

STEP 1

Assumptions1. We are given four equations that are essentially the same, just rearranged. . We need to solve for $x$ and $y$ in terms of the other variable.
3. The equations are linear and have a unique solution.

STEP 2

Let's start by solving the first equation for $x$ .
$x +6y =24$

STEP 3

To isolate $x$ , we need to subtract $6y$ from both sides of the equation.
$3x =24 -6y$

STEP 4

Now, divide both sides by $3$ to solve for $x$ .
$x = \frac{24 -6y}{3}$

STEP 5

implify the equation for $x$ .
$x =8 -2y$

STEP 6

Now, let's solve the second equation for $y$ .
$6y =24 -3x$

STEP 7

To isolate $y$ , we need to divide both sides of the equation by $6$ .
$y = \frac{24 -3x}{6}$

STEP 8

implify the equation for $y$ .
$y =4 - \frac{1}{2}x$

STEP 9

The third and fourth equations are just rearrangements of the first two equations, so they will yield the same solutions for $x$ and $y$ .
So, the solutions are $y =4 - \frac{}{2}x$ $x =8 -2y$

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QuestionSolve 3x+6y=243x + 6y = 243x+6y=24 for xxx and yyy. Find both xxx and yyy in terms of each other.

Studdy Solution

STEP 1

Assumptions1. We are given four equations that are essentially the same, just rearranged. . We need to solve for xxx and yyy in terms of the other variable.3. The equations are linear and have a unique solution.

STEP 2

Let's start by solving the first equation for xxx.x+6y=24x +6y =24x+6y=24

STEP 3

To isolate xxx, we need to subtract 6y6y6y from both sides of the equation.3x=24−6y3x =24 -6y3x=24−6y

STEP 4

Now, divide both sides by 333 to solve for xxx.x=24−6y3x = \frac{24 -6y}{3}x=324−6y​

STEP 5

implify the equation for xxx.x=8−2yx =8 -2yx=8−2y

STEP 6

Now, let's solve the second equation for yyy.6y=24−3x6y =24 -3x6y=24−3x

STEP 7

To isolate yyy, we need to divide both sides of the equation by 666.y=24−3x6y = \frac{24 -3x}{6}y=624−3x​

STEP 8

implify the equation for yyy.y=4−12xy =4 - \frac{1}{2}xy=4−21​x

STEP 9

The third and fourth equations are just rearrangements of the first two equations, so they will yield the same solutions for xxx and yyy.So, the solutions arey=4−2xy =4 - \frac{}{2}xy=4−2​xx=8−2yx =8 -2yx=8−2y

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QuestionSolve $3x + 6y = 24$ for $x$ and $y$ . Find both $x$ and $y$ in terms of each other.

Assumptions1. We are given four equations that are essentially the same, just rearranged. . We need to solve for $x$ and $y$ in terms of the other variable.
3. The equations are linear and have a unique solution.

Let's start by solving the first equation for $x$ .
$x +6y =24$

To isolate $x$ , we need to subtract $6y$ from both sides of the equation.
$3x =24 -6y$

Now, divide both sides by $3$ to solve for $x$ .
$x = \frac{24 -6y}{3}$

implify the equation for $x$ .
$x =8 -2y$

Now, let's solve the second equation for $y$ .
$6y =24 -3x$

To isolate $y$ , we need to divide both sides of the equation by $6$ .
$y = \frac{24 -3x}{6}$

implify the equation for $y$ .
$y =4 - \frac{1}{2}x$

The third and fourth equations are just rearrangements of the first two equations, so they will yield the same solutions for $x$ and $y$ .
So, the solutions are $y =4 - \frac{}{2}x$ $x =8 -2y$