Answer:
Solutions are (6,3) and (-2,3).
Step-by-step explanation:
From the first equation given we can write:
substituting for in the second equation given we get
∴ y=3
Putting y=3 in the first equation we get
x-2 = ±4
Hence x=6 or x=-2.
What does 16=c+(-5) equal? And how do you get to that answer?
2 answers:
You might be interested in
Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.