Question

2x+y-3z by y+3x =x by 2y. Find the value of z when x=1 and y=4

Answer 1

Answer:

$\mathsf {z = \frac{41}{24}}$

Step-by-step explanation:

$\textsf {Given :}$

$\mathsf {\frac {2x + y - 3z}{y + 3x} = \frac{x}{2y} }$

$\textsf {Substituting the values given (x = 1, y = 4) :}$

$\mathsf {\frac {2(1) + 4 - 3z}{4 + 3(1)} = \frac{1}{2(4)} }$

$\mathsf {\frac {6 - 3z}{7} = \frac{1}{8} }$

$\textsf {Cross multiply the values :}$

$\mathsf {8(6 - 3z) = 7}$

$\mathsf {48 - 24z = 7}$

$\mathsf {24z = 41}$

$\mathsf z = {\frac{41}{24}}$

Answer 2

Answer:

$z=\dfrac{41}{24}$

Step-by-step explanation:

Given equation:

$\dfrac{2x + y - 3z}{y + 3x} = \dfrac{x}{2y}$

Given:

• $x=1$

• $y=4$

Substitute the given values of x and y into the given equation:

$\implies \dfrac{2(1) + 4 - 3z}{4 + 3(1)} = \dfrac{1}{2(4)}$

$\implies \dfrac{6-3z}{7}=\dfrac{1}{8}$

Cross multiply:

$\implies 8(6-3z)=7$

Expand the brackets:

$\implies 48-24z=7$

Subtract 48 from both sides:

$\implies -24z=-41$

Divide both sides by -24:

$\implies z=\dfrac{41}{24}$