Expert: Scott A Wilson - 5/25/2010

Question
How do you find the solution of the system
3x-y=7
4x+y=7
can you show me in every way please and thankyou

Answer
Add the two equation together.
This will give 3x - y + 4x + y = 7 + 7.

On the left side, put like terms together.  On the right, 7+7=14.
That is, 3x + 4x - y + y =14.
Next, we get (3+4)x + (-1+1)y = 14.
Since 3+4=7 and -1+1=0, we have 7x = 14.

Dividing both sides by 7 at this point gives the answer for x, so x = 14/7.
We both know that this is x = 2.

Take this value and put it in the 1st equation, giving 3(2) - y = 7.
We also both know that 3*2 = 6, so we have 6 - y = 7.
Now if 6 is subtracted from both sides, we get -y = 7-6.
We also both know that 7-6=1, so we have -y = 1.

Since we're looking for y, mulitiply both sides by -1.
This gives y = -1.

Adding y to both sides of the 1st equation gives 3x = 7 + y.
Adding y to both sides of the 2nd equation gives 4x = 7 - y.

Since y = -1, they become 3x = 6 and 4x = 8.
Dividing the first by 3 on both sides gives x = 6/3.  We both know that 6/3 = 2.
To check this, we divide both sides by 4 in the 2nd equation.  This gives x = 8/4.
And finally, we both know that 8/4 is also 2, which agrees with the 1st equation.

Thus, we have found both x and y in the above explanation of the problem.