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6x – 2y = 2
8x + 3y = 14. Explain how knowing how to find the least common multiple (LCM) of two numbers can help you solve the system of equations presented here by eliminating the x-terms.

Respuesta :

The LCM of 6 and 8 is 24. Knowing this, multiply the first equation by 4 and the second by −3 to get opposite coefficients. Then, add the equations to eliminate x.

abidemiokin

The solution to the system of equation is (1, 2) using the least common multiple (LCM) of two numbers.

Given the simultaneous equation

6x – 2y = 2

8x + 3y = 14

Using the Elimination method to eliminate the x term. To do that we will use the common multiple of the product of the coefficients of x in both equations.

LCM of the coefficient of x in both equation = 6 * 8 = 48

Since 6 and 8 are multiples of 48, then we will multiply equation 1 by 8 and equation 2 by 8 as shown:

6x – 2y = 2 ........ 1 * 8

8x + 3y = 14 .......2 * 6

_______________________________

48x - 16y = 16

48x + 18y = 64

Subtract

-16y - 18y = 16 - 84

-34y = - 68

y = 68/34

y = 2

Substitute y = 2 into equation 1:

From 1:

6x - 2y = 2

6x - 2(2) = 2

6x - 4 = 2

6x = 2+4

6x = 6

x = 6/6

x = 1

Hence the solution to the system of equation is (1, 2)

Learn more here: https://brainly.com/question/22693341

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