Question

3. Find the point of intersection of the graphs for each system. a) x - y = 1 and 3x - y = -1​

Answer 1

Hello !

`\begin{cases} x - y &=1 \\ 3x-y &= - 1 \end{cases} \\\Leftrightarrow \begin{cases} x =y + 1 \\ 3x-y = - 1 \: \: \: \: \: (a)\end{cases}`

We replace x by y+1 in (a) :

`3(y + 1) - y = - 1 \\ 3y + 3 - y = - 1 \\ 2y = - 4 \\ y = ( - 4)/(2) = - 2`

Now we replace x by -1 in the first equation.

`x + 2 = 1 \\ x = -1`

The point of intersection is (-1;-2).

Have a nice day

Answer 2

the point of intersection is (-1 , -2)

Explanation:

`\begin{cases}x-y=1&(1)\\ 3x-y=-1&(2)\end{cases}`

(2) - (1) ⇒ (3x - y) - (x - y) = (-1) - 1

⇒ 3x - y - x + y = -2

⇒ 3x - x = -2

⇒ 2x = -2

⇒ x = -1

……………………………

Now ,we can determine the value of y

by substituting x by its value -1 in the first equation (1) :

(1) x - y = 1 ⇒-1 - y = 1 ⇒ -y = 2 ⇒ y = -2

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Conclusion:

x = -1

y = -2

Then ,the point of intersection of the graphs is (-1 , -2)