Question

Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated? One-fifth x three-fourths y = 9 Two-thirds x minus five-sixths y = 8 –10 times the first equation and 3 times the second equation 10 times the first equation and 3 times the second equation –3 times the first equation and 5 times the second equation 3 times the first equation and 5 times the second equation.

Answer 1

In the elimination method, one variable is eliminated from the system of equations to find the value of the other.

The first equation must be multiplied by 18 and the second equation must be multiplied by 8.

What is the elimination method?

To solve the system of equations and find the value of the variables, the elimination method is used.

In this method, one variable is eliminated from the system of equations to find the value of the other.

Given information-

The system of the equation given in the problem is,

$\rm \dfrac{1}{5}x+\dfrac{3}{4}y=9$

Let the above equation as equation 1.

The second equation given in the problem is,

$\rm \dfrac{2}{3}x-\dfrac{5}{6}y=8$

Let the above equation as equation 2.

To eliminate the y term, make the coefficient of y of both equations equal.

As the coefficient of x of equation 2 is 2/3.  

Thus multiply the second equation with 3 to eliminate the coefficient. Thus,

$\rm 3\times \dfrac{2}{3}x-3\times \dfrac{5}{6}y=3 \times 8\\\\2}x-\dfrac{5}{2}y=24$

Multiply equation 10 with 4 to make the coefficient of y equal. Thus,

$\rm -10\times \dfrac{1}{5}x-10\times \dfrac{3}{4}y=9\times -10\\\\-2x-\dfrac{15}{2}y=-90$

Adding both the equations

$\rm 2x-\dfrac{5}{2}y-2x-\dfrac{15}{2}y=24-90\\\\ \dfrac{-5}{2}y-\dfrac{-15}{2}y=-66$

Hence, the first equation must be multiplied by -10 and the second equation must be multiplied by 3.

Learn more about the elimination method here;

brainly.com/question/7013345

Answer 2

I know Im 2 weeks late but the answer is B. :) Have a good day .