raebaby420
Please Help c:
What are the solutions to the following system of equations?
y = x2 + 12x + 30
8x − y = 10
(−4, −2) and (2, 5)
(−2, −4) and (2, 5)
(−2, −4) and (5, 2)
No Real Solutions
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raebaby420
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What is the solution to the following system of equations?
y = x2 + 10x + 11
y = x2 + x − 7
(−2, −5)
(2, −5)
(−2, 5)
campbell_st
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5
rewrite the 2nd equation with y as the subject
y = 8x - 10
now equate it to the 1st equation and you get
\[8x - 10 = x^2 + 12x + 10\]
now you have 1 equation in 1 unknown to solve
myko
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y = x2 + 12x + 30
8x − y = 10
express y from second equation: \(y=8x-10\)
substitute in the 1º equation: \(8x-10=x^2 + 12x + 30\)
rearange terms: \(x^2+4x+40=0\)
solve this. You will get 2 solutions, which later substitute in the 2º equation to get corresponding y value
campbell_st
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5
oops should be '
\[8x - 10 = x^2 + 12x + 30\]
just solve for x
raebaby420
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Mm.. ill try. One sec, ill let you know what I get
missMob
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:O maths
campbell_st
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5
and can you check your equations as they may be a typo in them...
nirmalnema
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you can get the ans by by making the quadratic eq..in x
missMob
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we will put all the x on one side
raebaby420
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The what? LOL
campbell_st
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5
because based on the information there are any solutions that are real numbers
campbell_st
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5
oops... which is an option
campbell_st
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5
sorry...
raebaby420
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Ok.. so its D.. cool
missMob
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maths is confusing
raebaby420
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But idk how to get D
missMob
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*takes out the gun shoots maths*
campbell_st
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5
well do you know about the discriminant...? thats how you check...
raebaby420
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lol...
raebaby420
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No.. but I got 8x-10=x2+12x+30 so far..
raebaby420
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What do I do from there?
campbell_st
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5
subtract 8x from both sides...
then add 10 to both sides of the equation...
raebaby420
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Oh.. I knew that. For some reason I thought I needed to bring my X from the right to the left.
raebaby420
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Ok.. so I got x=x2+4x+40
Is that right?
nirmalnema
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ya you got it right
campbell_st
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5
and the discriminant is for a quadratic
\[ax^2 + bx + c = 0\]
thew discriminant is
\[b^2 - 4ac\]
you have a = 1, b = 4 and c = 40
it will be less than zero... meaning complex roots
raebaby420
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Sooo its D.
raebaby420
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Thanks everyone! c: