Solved on Dec 06, 2023

Solve the system of linear equations: $19-5x=54$ and $5=8+x/3$ .

STEP 1

Assumptions
1. We need to solve two separate equations for the variable $x$ .
2. The first equation is $19 - 5x = 54$ .
3. The second equation is $5 = 8 + \frac{x}{3}$ .

STEP 2

Let's solve the first equation for $x$ . We start by isolating the term containing $x$ on one side of the equation.
$19 - 5x = 54$

STEP 3

Subtract 19 from both sides of the equation to move the constant term to the right side.
$-5x = 54 - 19$

STEP 4

Calculate the result on the right side of the equation.
$-5x = 35$

STEP 5

Now, divide both sides of the equation by $-5$ to solve for $x$ .
$x = \frac{35}{-5}$

STEP 6

Calculate the value of $x$ .
$x = -7$
The solution to the first equation is $x = -7$ .

STEP 7

Now, let's solve the second equation for $x$ .
$5 = 8 + \frac{x}{3}$

STEP 8

Subtract 8 from both sides of the equation to isolate the term containing $x$ on one side.
$5 - 8 = \frac{x}{3}$

STEP 9

Calculate the result on the left side of the equation.
$-3 = \frac{x}{3}$

STEP 10

Multiply both sides of the equation by 3 to solve for $x$ .
$3 \times (-3) = x$

STEP 11

Calculate the value of $x$ .
$x = -9$
The solution to the second equation is $x = -9$ .

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Solve the system of linear equations: $19-5x=54$ and $5=8+x/3$ .

STEP 1

Assumptions
1. We need to solve two separate equations for the variable $x$ .
2. The first equation is $19 - 5x = 54$ .
3. The second equation is $5 = 8 + \frac{x}{3}$ .

STEP 2

Let's solve the first equation for $x$ . We start by isolating the term containing $x$ on one side of the equation.
$19 - 5x = 54$

STEP 3

Subtract 19 from both sides of the equation to move the constant term to the right side.
$-5x = 54 - 19$

STEP 4

Calculate the result on the right side of the equation.
$-5x = 35$

STEP 5

Now, divide both sides of the equation by $-5$ to solve for $x$ .
$x = \frac{35}{-5}$

STEP 6

Calculate the value of $x$ .
$x = -7$
The solution to the first equation is $x = -7$ .

STEP 7

Now, let's solve the second equation for $x$ .
$5 = 8 + \frac{x}{3}$

STEP 8

Subtract 8 from both sides of the equation to isolate the term containing $x$ on one side.
$5 - 8 = \frac{x}{3}$

STEP 9

Calculate the result on the left side of the equation.
$-3 = \frac{x}{3}$

STEP 10

Multiply both sides of the equation by 3 to solve for $x$ .
$3 \times (-3) = x$

STEP 11

Calculate the value of $x$ .
$x = -9$
The solution to the second equation is $x = -9$ .

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Solve the system of linear equations: 19−5x=5419-5x=5419−5x=54 and 5=8+x/35=8+x/35=8+x/3.

STEP 1

Assumptions1. We need to solve two separate equations for the variable xxx.2. The first equation is 19−5x=5419 - 5x = 5419−5x=54.3. The second equation is 5=8+x35 = 8 + \frac{x}{3}5=8+3x​.

STEP 2

Let's solve the first equation for xxx. We start by isolating the term containing xxx on one side of the equation.19−5x=5419 - 5x = 5419−5x=54

STEP 3

Subtract 19 from both sides of the equation to move the constant term to the right side.−5x=54−19-5x = 54 - 19−5x=54−19

STEP 4

Calculate the result on the right side of the equation.−5x=35-5x = 35−5x=35

STEP 5

Now, divide both sides of the equation by −5-5−5 to solve for xxx.x=35−5x = \frac{35}{-5}x=−535​

STEP 6

Calculate the value of xxx.x=−7x = -7x=−7The solution to the first equation is x=−7x = -7x=−7.

STEP 7

Now, let's solve the second equation for xxx.5=8+x35 = 8 + \frac{x}{3}5=8+3x​

STEP 8

Subtract 8 from both sides of the equation to isolate the term containing xxx on one side.5−8=x35 - 8 = \frac{x}{3}5−8=3x​

STEP 9

Calculate the result on the left side of the equation.−3=x3-3 = \frac{x}{3}−3=3x​

STEP 10

Multiply both sides of the equation by 3 to solve for xxx.3×(−3)=x3 \times (-3) = x3×(−3)=x

STEP 11

Calculate the value of xxx.x=−9x = -9x=−9The solution to the second equation is x=−9x = -9x=−9.

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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 system of linear equations: $19-5x=54$ and $5=8+x/3$ .

Assumptions
1. We need to solve two separate equations for the variable $x$ .
2. The first equation is $19 - 5x = 54$ .
3. The second equation is $5 = 8 + \frac{x}{3}$ .

Let's solve the first equation for $x$ . We start by isolating the term containing $x$ on one side of the equation.
$19 - 5x = 54$

Subtract 19 from both sides of the equation to move the constant term to the right side.
$-5x = 54 - 19$

Calculate the result on the right side of the equation.
$-5x = 35$

Now, divide both sides of the equation by $-5$ to solve for $x$ .
$x = \frac{35}{-5}$

Calculate the value of $x$ .
$x = -7$
The solution to the first equation is $x = -7$ .

Now, let's solve the second equation for $x$ .
$5 = 8 + \frac{x}{3}$

Subtract 8 from both sides of the equation to isolate the term containing $x$ on one side.
$5 - 8 = \frac{x}{3}$

Calculate the result on the left side of the equation.
$-3 = \frac{x}{3}$

Multiply both sides of the equation by 3 to solve for $x$ .
$3 \times (-3) = x$

Calculate the value of $x$ .
$x = -9$
The solution to the second equation is $x = -9$ .