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3 years ago

2/3x + 2= 21/3 solve for x a. 0 b. 1/2 c -2 d. 2

Mathematics

1 answer:

Helen [10]3 years ago

8 0

Answer:

x = 7.5

Step-by-step explanation:

2/3x + 2= 21/3

Subtract 2 from each side

2/3x + 2-2= 21/3-2

2/3x = 21/3 - 6/3

2/3x =15/3

2/3x = 5

Multiply each side by 3/2 to isolate x

2/3x * 3/2 = 5 *3/2

x = 15/2

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What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

3 years ago

Is x=-2 a solution for the equation below?

Misha Larkins [42]

Answer:

Step-by-step explanation:

-7+x^2-3x = 9+x-10

-7+(-2)^2-3*(-2) 9+(-2)-10

-7+4+6 9-12

3 > -3

if we substitute -2 to x, answer is not equal

3 0

3 years ago

Read 2 more answers

Write an equation that passes through the point (1, 3) and is perpendicular to x – 2y = -8.

Umnica [9.8K]

Answer:

y = -2x + 5

Step-by-step explanation:

Given:

Passes through point (1, 3)

Perpendicular to x – 2y = -8

Solve:

x – 2y = -8

y = 1/2x + 4

The slope is m = 1/2

The slope of the perpendicular line is the inverse of the slope of the original equation.

The slope of the inverse equation is m = -2.

Making an inverse equation of y = -2x + a

Find a:

Use point, (1, 3) where (x, y):

3 = (-2)*(1) + a

a = 5

y = -2x + 5

4 0

3 years ago

Read 2 more answers

What is the following number in decimal form?

aleksley [76]

8.8 because you need to multiply 1.68 by 10 which is 16.8-8=8.8

6 0

3 years ago

Math school is selling tickets to a play on the first day of ticket sales the school sold two adult tickets and three students t

Illusion [34]

Answer: the cost of an adult ticket is $9.

The cost of a child's ticket is $13

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one student ticket.

On the first day of ticket sales, the school sold two adult tickets and three students tickets for a total of $57. It means that

2x + 3y = 57- - - - - - - - - -1

The school took and $70 on the second day by selling two adult tickets and four student tickets. It means that

2x + 4y = 70- - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

- y = - 13

y = 13

Substituting y = 13 into equation 1, it becomes

2x + 3 × 13 = 57

2x + 39 = 57

2x = 57 - 39 = 18

x = 18/2

x = 9

8 0

3 years ago