Question

Graph the system of linear equations. -1/2y=1/2x+5 and y=2x+2

Answer 1

Answer:

The point for the given linear equations is ($\dfrac{-2}{3}$ , $\dfrac{2}{3}$)

Step-by-step explanation:

Given as :

The two linear equations are

First equation

$\dfrac{-1}{2}$ y = $\dfrac{1}{2}$ x + 5

Or,  $\dfrac{1}{2}$ y + $\dfrac{1}{2}$ x + 5 = 0

Taking LCM we get

y + x + 10 = 0          .......1

Second equation

y = 2 x + 2               ........2

Now solving both equation

Putting the value of y from eq 2 into eq 1

(2 x + 2) + x + 10 = 0

Or, 3 x + 12 = 10

Or, 3 x = 10 - 12

Or, 3 x = - 2

∴  x = $\dfrac{-2}{3}$

Now putting the value of x into eq 2

∵ y = 2 x + 2              

Or, y = 2 × $\dfrac{-2}{3}$ + 2

Or, y = $\dfrac{-4}{3}$ + 2

Or, y = $\dfrac{- 4 + 6}{3}$

∴   y = $\dfrac{2}{3}$

So, The points are (x , y ) = ($\dfrac{-2}{3}$ , $\dfrac{2}{3}$)

Now, plotting the points on x-y coordinate graph

Hence, The point for the given linear equations is ($\dfrac{-2}{3}$ , $\dfrac{2}{3}$) Answer