Question

if x=3t-8 and y=4+t, what equation expresses y in terms of x?

Answer 1

If x = 3t - 8 and y = 4 + t , then the equation $y=\frac{x}{3}+\frac{20}{3}$ represents variable y in terms of x.

Solution:

Given two equations are

x = 3t - 8   ------(1)

y = 4 + t    ------(2)

Need to determine the equation which express y in terms of x.

If we observer the two equations, common variable between the two is variable t.

So let’s first get the value of t in terms of x from equation 1.

$\begin{array}{l}{x=3 t-8} \\\\ {=>-3 t=-8-x} \\\\ {=>t=\frac{-8-x}{-3}=\frac{x+8}{3}} \\\\ {=>t=\frac{x+8}{3}}\end{array}$

$\text {On substituting } t=\frac{x+8}{3} \text { in equation }(2), \text { we get }$

$\begin{array}{l}{y=4+\frac{x+8}{3}} \\\\ {=>y=\frac{12+x+8}{3}} \\\\ {=>y=\frac{x+20}{3}} \\\\ {y=\frac{x}{3}+\frac{20}{3}} \\\\ y=0.334x+6.67}\end{array}$

Hence equation $y=\frac{x}{3}+\frac{20}{3}$ represents variable y in terms of x.