Answer:
The two solutions in exact form are:
and
.
If you prefer to look at approximations just put into your calculator:
and
.
Step-by-step explanation:
I guess you are asked to find the solution the given system.
I'm going to use substitution.
This means I'm going to plug the second equation into the first giving me:
I replaced the 1st y with what the 2nd y equaled.
Before we continue solving this I'm going to expand the using the following:
.
Let's go back to the equation we had:
After expansion of the squared binomial we have:
Combine like terms (doing the part:
Subtract 36 on both sides:
Simplify the 25-36 part:
Compare this to which is standard form for a quadratic.
We should see the following:
The formula that solves this equation for the variable is:
Plugging in our values for give us:
Simplify the bottom; that is 2(10)=20:
Put the inside of square root into the calculator; that is put in the calculator:
Side notes before continuation:
Let's see if 1340 has a perfect square.
I know 1340 is divisible by 10 because it ends in 0.
1340=10(134)
134 is even so it is divisible by 2:
1340=10(2)(67)
1340=2(2)(5)(67)
1340=4(5)(67)
1340=4(335)
4 is a perfect square so we can simplify the square root part further:
.
Let's go back to the solution:
Now I see all three terms contain a common factor of 2 so I'm going to divide top and bottom by 2:
So we have these two x values:
Now we just need to find the corresponding y-coordinate for each pair of points.
I'm going to use the easier equation .
Let's do it for the first x I mentioned:
If then
.
Let's simplify:
Distribute the -3 to the terms on top:
Combine the two terms; I'm going to do this by writing 5 as 50/10:
Combine like terms on top; the -45+50 part:
.
So one solution point is:
.
Let's find the other one for the other x that we got.
If then
.
Let's simplify.
Distribute the -3 on top:
I'm going to write 5 as 50/10 so I can combine the terms as one fraction:
Simplify the -45+50 part:
.
So the other point of intersection is:
.
The two solutions in exact form are:
and
.
If you prefer to look at approximations just put into your calculator:
and
.