Question 105

If 2x+y= 15, 2y+z= 25 and 2z+x =26 ,what is value of z?

Solution

Equation (i) : $$2x+y=15$$

Equation (ii) : $$2y+z=25$$

Equation (iii) : $$2z+x=26$$

Adding the three equations, => $$3x+3y+3z=15+25+26$$

=> $$3(x+y+z)=66$$

=> $$x+y+z=\frac{66}{3}=22$$ ------------(iv)

Subtracting equation (i) from (iv), => $$(z)+(x-2x)+(y-y)=(22-15)$$

=> $$z-x=7$$ -------------(v)

Adding equations (v) and (iii), => $$3z=26+7=33$$

=> $$z=\frac{33}{3}=11$$

=> Ans - (E)

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