Solve for x: 3x - 5 = 2x + 6.<br> Your 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

The number 40 can be written as the product of a prime factor like 40=2×2×2×5 . Write the number 100 as a product of its prime f

Vladimir79 [104]

Answer

The answer to your question is 2 x 2 x 5 x 5 or 2² 5²

Step-by-step explanation:

Process

1.- To find the prime factors of a number, we must divide the number by prime numbers like 2, 3, 5, 7, 11, etc. starting from the lowest number.

100 2

50 2

25 5

5 5

1

Then 100 = 2 x 2 x 5 x 5 or 2² 5²

5 0

3 years ago

Factor 2x2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors.

zlopas [31]

9514 1404 393

Answer:

rewrite: 2x^2 +5x +20x +50
factored: (x +10)(2x +5)

Step-by-step explanation:

I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.

You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.

100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10

The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.

The trinomial can be rewritten using these factors as ...

2x^2 +5x +20x +50

Then it can be factored by grouping consecutive pairs:

(2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)

_____

<em>Additional comment</em>

It doesn't matter which of the factors of the pair you write first. If our rewrite were ...

2x^2 +20x +5x +50

Then the grouping and factoring would be (2x^2 +20x) +(5x +50)

= 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring

6 0

2 years ago

Solve for x: 3x - 5 = 2x + 6. Your answer