The sum of two numbers is -3. five times the first number equals 3 times the second number. find the two numbers
1 answer:
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Answer:
Step-by-step explanation:
Let's examine the following general product of two binomials with variables x and y in different terms:
so we want the following to happen:
Notice as well that means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product
, then we can consider the case in which one of this (b or d) is the negative factor. So let's then assume that
are positive.
We can then try combinations for such as:
Just by selecting the first one
we get that
and since
This quadratic equation give as one of its solutions the integer: d = -2, and consequently,
Now we have a good combination of parameters to render the factoring form of the original trinomial:
which makes our factorization:
Question 1:
y=-x+7
y=2x-2
(-x+7)=2x-2
-x+7+x=2x-2+x
7=2x-2+x
7+2=2x-2+x+2
9=3x
9/3=3x/3
3=x
y=-x+7
y=-(3)+7
y=4
Question 2:
y-1=2x
y+2x=5
y-1=2x
y-1+1=2x+1
y=2x
(2x+1)+2x=5
2x+1+2x=5
4x+1=5
4x+1-1=5-1
4x=4
4x/4=4/4
x=1
y-1=2(1)
y-1+1=2+1
y=3
Answer: x=1 y=3
y=-x+7
y=2x-2
(-x+7)=2x-2
-x+7+x=2x-2+x
7=2x-2+x
7+2=2x-2+x+2
9=3x
9/3=3x/3
3=x
y=-x+7
y=-(3)+7
y=4
Question 2:
y-1=2x
y+2x=5
y-1=2x
y-1+1=2x+1
y=2x
(2x+1)+2x=5
2x+1+2x=5
4x+1=5
4x+1-1=5-1
4x=4
4x/4=4/4
x=1
y-1=2(1)
y-1+1=2+1
y=3
Answer: x=1 y=3