1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vlada [557]
3 years ago
13

How many Solutions does this system have? (1 point)

Mathematics
1 answer:
mixas84 [53]3 years ago
5 0

The given system of equation that is 2x+y=3 and 6x=9-3y has infinite number of solutions.

Option -C.

<u>Solution:</u>

Need to determine number of solution given system of equation has.

\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}

Let us first bring the equation in standard form for comparison

\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}

\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

To check how many solutions are there for system of equations a_{1} x+b_{1} y+c_{1}=0 \text{ and }a_{2} x+b_{2} y+c_{2}=0, we need to compare ratios of \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}

In our case,  

a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3

a_{2}  = 6, b_{2} = 3,\text{ and }c_{2} = -9

\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}

As \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}, so given system of equations have infinite number of solutions.

Hence, we can conclude that system has infinite number of solutions.

You might be interested in
Find the slope of the line that passes through the<br> points (-4, 7) and (3,-2)
schepotkina [342]

Answer:

-9/7

Step-by-step

Slope Formula:

\frac{y_2-y_1}{x_2-x_1}

We can plug in the numbers 7 and -2 for the y and -4 and 3 for x

\frac{7-(-2)}{-4-3} =\frac{9}{-7}

8 0
2 years ago
What is the value of d in 3/4(8x-6)-2=1/2-x
Salsk061 [2.6K]

Answer: 32/35

Step-by-step explanation:

got it correct

7 0
2 years ago
To increase an amount by 7%, what single multiplier would you use ?
Scrat [10]
You would use 1.07 for that
6 0
3 years ago
Read 2 more answers
A farmer wants to net at least $10,000/acre on the sale of his 80-acre property. If he allows for a total of 10% for commissions
lara [203]

Answer:

$11,111.11

Step-by-step explanation:

Net Money farmer wanted to get the on selling 1 acre = $10,000

Percentage of commission and closing cost incurred by him = 10%

out of 100 %, he will incur cost of 10%,

rest of them will be with him.

In percentage money he would have be = (100 - 10)% = 90%

Thus, 90 % will be net money he would have.

Let the list price be $x

Given that 90% of this $x will be with farmer which is equal to

90% of x = 90/100 * x = 0.9 x

It is given that he wants to net $10000

so 0.9x = $10,000

=> x =  $10,000/0.9 = $11,111.11.

Listing price per acre should be at least  $11,111.11.

5 0
2 years ago
ILL GIVE U BRAINLYIST
s2008m [1.1K]

Answer:

D

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Find the amplitude y = 5 sin one half x.
    5·1 answer
  • ASAP PLEASE ANSWER quadrilateral ABCD is dilated at center (0,0) with scale factor 1/2 to form quadrilateral A'B'C'D'. wha is th
    15·2 answers
  • From eight different books, in how many ways can any four of them be arranged side by side on a bookshelf?
    11·1 answer
  • 3080.34 rounded to the nearest whole number
    9·2 answers
  • What is 2,034,627,105 rounded to the nearest ten thousand
    6·1 answer
  • Graph the line with 3/4 slope<br> passing through the point (2,-2).
    8·1 answer
  • Choose all true statements.
    12·2 answers
  • Which of the following types of statements can justify the steps of a proof?
    13·2 answers
  • The equation y+6=1/3(x-9) is written in point- slope form. What is the equation written in slope-intercept form?
    10·1 answer
  • 48/4+[6+{12/2 of 3}-4]+20​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!