Solved on Feb 21, 2024

Solve the linear equations: $-5a = -0.2$ , $b + 14.5 = 10$ , and $2 = -\frac{1}{5}c$ .

STEP 1

Assumptions
1. We are given three separate equations to solve: a. $-5a = -0.2$ b. $-b + 14.5 = 10$ c. $2 = -\frac{1}{5}c$
2. We need to solve for $a$ , $b$ , and $c$ in each equation respectively.

STEP 2

Start by solving the first equation for $a$ .
$-5a = -0.2$

STEP 3

Divide both sides of the equation by $-5$ to isolate $a$ .
$a = \frac{-0.2}{-5}$

STEP 4

Calculate the value of $a$ .
$a = \frac{-0.2}{-5} = 0.04$

STEP 5

Now, move on to the second equation to solve for $b$ .
$-b + 14.5 = 10$

STEP 6

Subtract $14.5$ from both sides of the equation to isolate $-b$ .
$-b = 10 - 14.5$

STEP 7

Calculate the value on the right side of the equation.
$-b = -4.5$

STEP 8

Multiply both sides by $-1$ to solve for $b$ .
$b = 4.5$

STEP 9

Finally, solve the third equation for $c$ .
$2 = -\frac{1}{5}c$

STEP 10

Multiply both sides of the equation by $-\frac{1}{5}$ to isolate $c$ .
$c = 2 \cdot -5$

STEP 11

Calculate the value of $c$ .
$c = -10$
The solutions to the equations are: $a = 0.04$ , $b = 4.5$ , and $c = -10$ .

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Solve the linear equations: $-5a = -0.2$ , $b + 14.5 = 10$ , and $2 = -\frac{1}{5}c$ .

STEP 1

Assumptions
1. We are given three separate equations to solve: a. $-5a = -0.2$ b. $-b + 14.5 = 10$ c. $2 = -\frac{1}{5}c$
2. We need to solve for $a$ , $b$ , and $c$ in each equation respectively.

STEP 2

Start by solving the first equation for $a$ .
$-5a = -0.2$

STEP 3

Divide both sides of the equation by $-5$ to isolate $a$ .
$a = \frac{-0.2}{-5}$

STEP 4

Calculate the value of $a$ .
$a = \frac{-0.2}{-5} = 0.04$

STEP 5

Now, move on to the second equation to solve for $b$ .
$-b + 14.5 = 10$

STEP 6

Subtract $14.5$ from both sides of the equation to isolate $-b$ .
$-b = 10 - 14.5$

STEP 7

Calculate the value on the right side of the equation.
$-b = -4.5$

STEP 8

Multiply both sides by $-1$ to solve for $b$ .
$b = 4.5$

STEP 9

Finally, solve the third equation for $c$ .
$2 = -\frac{1}{5}c$

STEP 10

Multiply both sides of the equation by $-\frac{1}{5}$ to isolate $c$ .
$c = 2 \cdot -5$

STEP 11

Calculate the value of $c$ .
$c = -10$
The solutions to the equations are: $a = 0.04$ , $b = 4.5$ , and $c = -10$ .

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Solve the linear equations: −5a=−0.2-5a = -0.2−5a=−0.2, b+14.5=10b + 14.5 = 10b+14.5=10, and 2=−15c2 = -\frac{1}{5}c2=−51​c.

STEP 1

Assumptions1. We are given three separate equations to solve: a. −5a=−0.2-5a = -0.2−5a=−0.2 b. −b+14.5=10-b + 14.5 = 10−b+14.5=10 c. 2=−15c2 = -\frac{1}{5}c2=−51​c2. We need to solve for aaa, bbb, and ccc in each equation respectively.

STEP 2

Start by solving the first equation for aaa.−5a=−0.2-5a = -0.2−5a=−0.2

STEP 3

Divide both sides of the equation by −5-5−5 to isolate aaa.a=−0.2−5a = \frac{-0.2}{-5}a=−5−0.2​

STEP 4

Calculate the value of aaa.a=−0.2−5=0.04a = \frac{-0.2}{-5} = 0.04a=−5−0.2​=0.04

STEP 5

Now, move on to the second equation to solve for bbb.−b+14.5=10-b + 14.5 = 10−b+14.5=10

STEP 6

Subtract 14.514.514.5 from both sides of the equation to isolate −b-b−b.−b=10−14.5-b = 10 - 14.5−b=10−14.5

STEP 7

Calculate the value on the right side of the equation.−b=−4.5-b = -4.5−b=−4.5

STEP 8

Multiply both sides by −1-1−1 to solve for bbb.b=4.5b = 4.5b=4.5

STEP 9

Finally, solve the third equation for ccc.2=−15c2 = -\frac{1}{5}c2=−51​c

STEP 10

Multiply both sides of the equation by −15-\frac{1}{5}−51​ to isolate ccc.c=2⋅−5c = 2 \cdot -5c=2⋅−5

STEP 11

Calculate the value of ccc.c=−10c = -10c=−10The solutions to the equations are: a=0.04a = 0.04a=0.04, b=4.5b = 4.5b=4.5, and c=−10c = -10c=−10.

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Solve the linear equations: $-5a = -0.2$ , $b + 14.5 = 10$ , and $2 = -\frac{1}{5}c$ .

Assumptions
1. We are given three separate equations to solve: a. $-5a = -0.2$ b. $-b + 14.5 = 10$ c. $2 = -\frac{1}{5}c$
2. We need to solve for $a$ , $b$ , and $c$ in each equation respectively.

Start by solving the first equation for $a$ .
$-5a = -0.2$

Divide both sides of the equation by $-5$ to isolate $a$ .
$a = \frac{-0.2}{-5}$

Calculate the value of $a$ .
$a = \frac{-0.2}{-5} = 0.04$

Now, move on to the second equation to solve for $b$ .
$-b + 14.5 = 10$

Subtract $14.5$ from both sides of the equation to isolate $-b$ .
$-b = 10 - 14.5$

Calculate the value on the right side of the equation.
$-b = -4.5$

Multiply both sides by $-1$ to solve for $b$ .
$b = 4.5$

Finally, solve the third equation for $c$ .
$2 = -\frac{1}{5}c$

Multiply both sides of the equation by $-\frac{1}{5}$ to isolate $c$ .
$c = 2 \cdot -5$

Calculate the value of $c$ .
$c = -10$
The solutions to the equations are: $a = 0.04$ , $b = 4.5$ , and $c = -10$ .