Find the distance between A(0,1)and B(-4,6) to the nearest tenth

Annette [7]

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

$4x-5y=3$

$3x+5y=13$

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Adding Equation 1 and Equation 2

$4x-5y+3x+5y=3+13$

$7x=16$

$x=$ $\frac{16}{7}$

Putting $x=$ $\frac{16}{7}$ in Equation [1]

$4x-5y=3$ $......[1]$

$y=$ $\frac{43}{35}$

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Solving the equation 2 for x variable

$3x=13-5y$

$x=\frac{13-5y}{3}$

Plugging $x=\frac{13-5y}{3}$ in equation [1]

$4(\frac{13-5y}{3}) -5y=3$

$y = \frac{43}{35}$

Putting $y = \frac{43}{35}$ in Equation 2

$3x+5y=13$ $......[2]$

$x = \frac{16}{7}$

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

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4 0

3 years ago

CD contains the points C at 4, D at 0, and E at 2.

horsena [70]

Answer:

the length of CD is 4

the length of DE is 2

the ratio of CD to DE is 2:1

Step-by-step explanation:

8 0

3 years ago

What is the difference between plotting (2, 3) and (3,2)<br> on a coordinate plane? Explain

Lunna [17]

Answer:

Step-by-step explanation:

2,3 has I lower unit than 3,2 let’s say that we plot it we see that 2,3 is lower down 3,2 :)

5 0

3 years ago

Read 2 more answers

3/6, 1/12, 3/6, 3/60 determine the lcd by division of prime number

viva [34]

Answer:

LCD = 60

<em>BRAINLIEST, PLEASE!</em>

Step-by-step explanation:

All of the denominator numbers are multiples of 60, and since 60 is also equal to the largest denominator number, it's the LCD.

7 0

3 years ago

Kiran and his cousin work during the summer for a landscaping company. Kiran's cousin has been working for the company longer, s

Marta_Voda [28]

Kiran earns $8.50 per hour.

Let x represent Kiran's pay. He worked 23 hours last week, so his pay would be given by 23x.

Kiran's cousin is paid 30% more. 30% = 30/100 = 0.3. We add this to the x per hour that Kiran is paid:

x + 0.3x = 1.3x

This is multiplied by 27, since Kiran's cousin works 27 hours:
27(1.3x)

This gives us the following equation:
23x + 27(1.3x) = 493.85
23x + 35.1x = 493.85
58.1x = 493.85

Divide both sides by 58.1:
58.1x/58.1 = 493.85/58.1
x = 8.5

Thus Kiran earns 8.50 per hour.

8 0

3 years ago