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finlep [7]
2 years ago
12

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

Mathematics
2 answers:
weeeeeb [17]2 years ago
7 0

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 =  \frac{ - 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

natima [27]2 years ago
5 0

Answer:

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

Step-by-step 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

========================

Conclusion:

x = -1

y = -2

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

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=============================================

To solve for y, we just have to substitute the value of x to any of the equation given above, that we feel comfortable with. And I'm going to choose this equation: 4x + 2y = 20


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The last thing you would do is to check if the answers is correct.
All you have to do is plug in the values of x and y into both equations and see if they equal to one another.

You may have to do this by yourself :P

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