What are the coordinates of the one point shared in common between the two linear functions given: y=2x-2, 3y=-x+15?

Nov 24, 2016

$\left(3 , 4\right)$

Explanation:

To find a common point, solve the equations $\textcolor{b l u e}{\text{simultaneously}}$

We are given y = 2x - 2. Substitute this value for y into the other equation and solve for x.

$\Rightarrow 3 \left(2 x - 2\right) = - x + 15$

distribute the bracket, collect terms in x on the left side and numeric values on the right side.

$\Rightarrow 6 x - 6 = - x + 15$

add x to both sides.

$6 x + x - 6 = \cancel{- x} \cancel{+ x} + 15$

$\Rightarrow 7 x - 6 = 15$

add 6 to both sides.

$7 x \cancel{- 6} \cancel{+ 6} = 15 + 6$

$\Rightarrow 7 x = 21$

To solve for x, divide both sides by 7

$\frac{\cancel{7} x}{\cancel{7}} = \frac{21}{7} \Rightarrow x = 3$

To find the corresponding value of y, substitute x = 3 into
y = 2x - 2

$\Rightarrow y = \left(2 \times 3\right) - 2 = 6 - 2 = 4$

$\Rightarrow \left(3 , 4\right) \text{ is a common point}$

Check :

Using x = 3 then y should be 4 for both equations.

$\Rightarrow y = 2 x - 2 = \left(2 \times 3\right) - 2 = 4 \leftarrow \text{ True}$

$\Rightarrow 3 y = - x + 15 = - 3 + 15 = 12 \Rightarrow y = 4 \leftarrow \text{ True}$

$\text{Thus" (3,4)" is a common point to both equations}$