Mathematics: Work out 6d + 8 = 14 + 3d

Work out 6d + 8 = 14 + 3d - id681437898362, absoul1143

AM28

30.05.2020

Their is the system of linear equations $\frac{1}{3} x+\frac{1}{4} y=1$ and 2x-3y=-30 .

The solution of the given system of equation is 8. The correct answer is option D.

Given equations:

$\frac{1}{3} x+\frac{1}{4} y=1$

2x-3y=-30

Let

$\frac{1}{3} x+\frac{1}{4} y=1$ ...........(i)

2x-3y=-30 ..........(ii)

Look for terms that can be eliminated. The equations do not have any x or y terms with the same coefficients.

Multiply the equation (i) by 12 so they do have the same coefficient.

$12(\frac{1}{3} x+\frac{1}{4} y=1)$

4x+3y=12 .............(iii)

Adding equation (ii) and equation (iii)

$2x-3y=-30\\4x+3y=12$

------------------------

$6x=-18\\x=\frac{-18}{6}\\x=-3$

Substitute x = -3 into one of the original equations to find y.

$2(-3)-3y=-30\\-6-3y=-30\\-3y=-30+6\\y=\frac{-24}{-3} \\y=8$

Therefore, the answer is the option D

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