Question

# Solve the following equations: 2x−4y+9z=28 7x+3y−5z=3 9x+10y−11z=4

A
x=2,y=3,z=4
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B
x=7,y=3,z=4
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C
x=2,y=3,z=5
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D
x=2,y=4,z=4
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Solution

## The correct option is A x=2,y=3,z=4 We have 2x−4y+9z=28...........(1) 7x+3y−5z=3............(2) 9x+10y−11z=4............(3) Multiplying equation (1) by 3, and (2) by 4, we have 6x−12y+27z=84...............(4) and 28x+12y−20z=12..........(5) Adding equations (4) and (5), we get 34x+7z=96............(6) Again, multiplying (2) by 10, and (3) by 3, we have 70x+30y−50z=30...............(7) and 27x+30y−33z=12..........(8) Subtracting equations (8) from (7), we get 43x−17z=18............(9) Now, we have 34x+7z=96........(6) 43x−17z=18........(9) Multiplying equation (6) by 17, and (9) by 7, we have 578x+119y=1632...............(10) and 301x−119y=126..........(11) Adding equations (10) and (11), we get 879x=1758 ⇒x=2 Putting x=2 in equation (9), we get 86−17z=18 ⇒17z=68 ⇒z=4 Putting x=2 and z=4 in equation (1), we get 4−4y+36=28 ⇒4y=12 ⇒y=3 Thus, we have x=2,y=3, and z=4

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