Final answer:
To find the value of x in terms of z, solve the given equations for y. Then, substitute the expression for y into the second equation and solve for x. The value of x in terms of z is (4/3)z.
Step-by-step explanation:
To find the value of x in terms of z, we need to eliminate y from the given equations. We can do this by solving the first equation for y in terms of x and substituting it into the second equation:
From the equation 3x = 2y, we can isolate y by dividing both sides of the equation by 2. This gives us y = (3/2)x. Substituting this value into the second equation, 5y = 6z, we get 5((3/2)x) = 6z. Simplifying this equation, we have (15/2)x = 6z. To solve for x, we divide both sides of the equation by (15/2), giving us x = (4/3)z.
Therefore, the value of x in terms of z is (4/3)z, which corresponds to option c.