contestada

As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?

5x + 6y = 18
2x – 3y = 12

Respuesta :

aklee18oo

Answer:

3

Step-by-step explanation:

First, we can start by multiplying the equation 2x - 3y = 12 by six to see where that gets us,

2x - 3y = 12 --> 12x - 18y = 72

12x - 18y = 72

5x + 6y = 18 (other equation)

We can notice that eliminating the y term would be the easiest to go about, so we want to find the number that we can multiply 6 by to get 18. That number is 3, so the factor is 3.

You can use the fact that non of 2 times 6 doesn't include 5 as factor.

There are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.

Those values of the factor are [tex]3[/tex]   (for elimination of y) or [tex]-\dfrac{12}{5}[/tex] (for elimination of x)

How to find by what factor should we multiply the equations to eliminate a variable in a system of linear equations of two or more variables?

Our aim in doing so is to make the coefficients of same variable equal and with opposite signs so that when we add the equations, that variable gets eliminated because of coefficient becoming zero.

For example, take the given equations and the factor by which Yumiko multiplied the second equation.

5x + 6y = 18

2x – 3y = 12 => 12x - 18y = 72   (since she multiplied this with 6)

Let she multiply the first equation with factor "p"

Then we will have the system as;

[tex]p \times 5x + p \times 6y = p \times 18\\12x - 18y = 72[/tex]

Adding both the equations, we get:

[tex](5p + 12)x + (6p - 18)y = 18p + 72[/tex]

Since there are two variables and since any one of them can be eliminated depending on the value of p, thus we have two cases:

  • Case 1: Eliminated variable is x

Then we have coefficient of x = 0

or

[tex]5p + 12 = 0\\5p = -12\\p = -\dfrac{12}{5}\\[/tex]

  • Case 2: Eliminated variable is y

Then we have coefficient of y = 0

or

[tex]6p - 18 = 0\\6p = 18\\p = \dfrac{18}{6} = 3[/tex]

Thus, there are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.

Those values of the factor are [tex]3[/tex]  or [tex]-\dfrac{12}{5}[/tex]

Learn more about system of linear equations here:

https://brainly.com/question/13722693

Otras preguntas