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baherus [9]
2 years ago
15

Solve for the indicated variable.

Mathematics
1 answer:
Hunter-Best [27]2 years ago
3 0

Answer:

<h3><u>1.</u>)</h3>

3n + 1 = 7n - 5

1 + 5 = 7n - 3n

6 = 4n

3/2 = n

<h3><u>2</u><u>.</u>)</h3>

2[x + 3(x - 1)] = 18

2[x + 3x - 3] = 18

2(4x - 3) = 18

8x - 6 = 18

8x = 12

x = 12/8

x = 3/2

<h3><u>3</u><u>.</u>)</h3>

6(y + 2) - 4 = -10

6y + 12 - 4 = -10

6y = -10 - 8

6y = -18

y = -3

<h3><u>4</u><u>.</u>)</h3>

2x² = 50

x² = 50/2

x = √25

x = 5

<h3><u>5</u><u>.</u>)</h3>

5 + 2(k + 4) = 5(k - 3) + 10

5 + 2k + 8 = 5k - 15 + 10

2k - 5k = -5 - 13

-3k = -18

k = 6

<h3><u>6</u><u>.</u>)</h3>

6 + 2x(x - 3) = 2x²

6 + 2x² - 6x = 2x²

-6x = 2x² - 2x² - 6

x = 1

<h3><u>7</u><u>.</u>)</h3>

2/3x - 18 = x/6

12(2/3x - 18 = x/6)

8x - 216 = 2x

8x - 2x = 216

6x = 216

x = 36

<h3><u>8.</u>)</h3>

x - 2/3 = 2x + 1/4

12(x - 2/3 = 2x + 1/4)

4x - 8 = 6x + 3

4x - 6x = 8 + 3

2x = 11

x = 11/2

<u>-TheUnknownScientist</u><u> 72</u>

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which ordered pair is a solution to the system of linear equations 1/2 x - 3/4 y = 11/60 and 2/5 x + 1/6 y = 3/10?
bekas [8.4K]

Value of x=\frac{2}{3}\,\,and\,\,value\,\,of\,\,y=\frac{1}{5}

Solution set is  (\frac{2}{3},\frac{1}{5})

Step-by-step explanation:

We need to solve the following system of equations:

\frac{1}{2}x-\frac{3}{4}y=\frac{11}{60}\,\,\,eq(1)\\\frac{2}{5}x+\frac{1}{6}y=\frac{3}{10}\,\,\,eq(2)

We can solve this using Substitution.

Isolate x in \frac{1}{2}x-\frac{3}{4}y=\frac{11}{60}

\frac{1}{2}x=\frac{11}{60}+\frac{3}{4}y\\ x=\frac{11}{30}+\frac{3}{2}y

Putting value of x in equation(2)

\frac{2}{5}(\frac{11}{30}+\frac{3}{2}y)+\frac{1}{6}y=\frac{3}{10}\\Solving:\\Taking\,\,LCM\,\,of\,\,5,6,10 \,\,we\,\,get: 30\\Multiply\,\,by\,\,LCM\\\frac{2}{5}(\frac{11}{30}+\frac{3}{2}y)\times30+\frac{1}{6}y\times30=\frac{3}{10}\times30\\Simplifying:\\12(\frac{11}{30}+\frac{3}{2}y)+5y=9\\\frac{22}{5}+18y+5y=9\\23y=9-\frac{22}{5}\\23y=\frac{45-22}{5}\\23y=\frac{23}{5}\\y=\frac{\frac{23}{5} }{23}\\y=\frac{1}{5}

Putting value of y=1/5 in x=\frac{11}{30}+\frac{3}{2}y

x=\frac{11}{30}+\frac{3}{2}\times\frac{1}{5} \\x=\frac{11}{30}+\frac{3}{10}\\x=\frac{11+3*3}{30}\\x=\frac{11+9}{30} \\x=\frac{20}{30}\\x=\frac{2}{3}

So, value of x=\frac{2}{3}\,\,and\,\,value\,\,of\,\,y=\frac{1}{5}

Solution set is  (\frac{2}{3},\frac{1}{5})

Keywords: System of linear Equations

Learn more about System of linear Equations at:

  • brainly.com/question/9045597
  • brainly.com/question/13168205
  • brainly.com/question/2115716

#learnwithBrainly

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