Question 45903: solve the system of equations
3x-4y=-3
6x+2z=-7/2
2y-4z=4
Answer by abhijitvakil(7)   (Show Source):
You can put this solution on YOUR website! Lets day the equations are numbered 1, 2 & 3 as under
3x - 4y = -3 ....... 1
6x + 2z = -7/2 ...... 2
2y - 4z = 4 ...... 3
The approach is to use one equation to express the value of one of the variables in terms of the other, and then use this value in another equation, as a result of which we get 2 equations in 2 variables, which can then be easily solved. Note -
Eq 3 is divided by 2 to give :
y - 2z = 2 ;
So we may write
y = 2 - 2z .... 4
Use this value of y in eq 1 above, we get
3x - 4(2-2z) = -3
or
3x - 8 + 8z = -3
or
3x + 8z = 5 ...... eq no 5
Multiply this equation by 2, we get
6x + 16z = 10 .... eq no 6
Subtract eq no 2 from eq no 6, we get
6x + 16z - 6x - 2z = 10 + 7/2
or
14z = 10 + 7/2
or
z = 10/14 + 7/(2*14)
or
z = 5/7 + 1/4 =27/28.
Use this value of z in eq 2 to get the value of x & eq 3 to get the value of y.
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