Question

Which ordered pair (x, y) is a solution to given system of linear equations?

Answer 1

Answer:

$(\frac{1}{6}, \frac{1}{2})$ or $(0.167,0.5)$

Step-by-step explanation:

Given

$3x + y =1$

$15x + y = 3$

Required

Determine the solution

We'll solve using elimination method.

Subtract the first equation from the second:

$15x + y = 3$

$3x + y =1$

$--------$

$15x - 3x + y - y = 3 - 1$

$15x - 3x + y - y = 3 - 1$

$15x - 3x = 3 - 1$

$12x = 2$

Make x the subject:

$x = \frac{2}{12}$

$x = \frac{1}{6}$

$x =0.167$

Substitute $\frac{1}{6}$ for x in the first equation

$3x + y =1$

$3(\frac{1}{6}) + y = 1$

$\frac{1}{2} + y = 1$

Make y the subject

$y = 1 -\frac{1}{2}$

$y = \frac{2-1}{2}$

$y = \frac{1}{2}$

$y = 0.5$

Hence, the solution is:

$(\frac{1}{6}, \frac{1}{2})$ or $(0.167,0.5)$