Answer:
(The solution is (4, -11).
Step-by-stp explanation:
Let f(x) = g(x) = y:
y = 3x − 23
y = -4.5x + 7 Subtract the second equation from the first to eliminate y:
0 = 7.5x - 30
7.5x = 30
x = 4
Plug this into the first equation:
y = 3(4) - 23
y = -11.
Answer:
7 and 1
Step-by-step explanation:
Let the numbers be a and b.
<u>A positive number is 7 times another number:</u>
<u>If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:</u>
<u>To solve this we substitute </u><u>a</u><u> with </u><u>7b</u><u> in the second equation:</u>
- 7b + 3 = 5/2 × (b +3) ⇒ multiplying both sides by 2
- 14b + 6 = 5b + 15 ⇒ collecting like terms
- 14b - 5b = 15 - 6
- 9b = 9
- b = 1 ⇒ solved for b
<u>Then, finding a:</u>
- a= 7b
- a=7*1
- a= 7 ⇒ solved for a
<u>So the numbers are</u> 7 and 1
Answer:
Step-by-step explanation:
Here, we add up two polynomials shown.
The polynomials are:
![[-m^2 + 6]+[-4m^2 +7m + 2]](https://tex.z-dn.net/?f=%5B-m%5E2%20%2B%206%5D%2B%5B-4m%5E2%20%2B7m%20%2B%202%5D)
In order to add up the 2 polynomials shown, we have to see the "like terms" and add them up.
We add up the "
" terms and the constant (number) terms. There is one term with "m", so we leave it like that. Let's add up. Shown below:\
![[-m^2 + 6]+[-4m^2 +7m + 2]\\=-m^2-4m^2+6+2+7m\\=-5m^2+7m+8](https://tex.z-dn.net/?f=%5B-m%5E2%20%2B%206%5D%2B%5B-4m%5E2%20%2B7m%20%2B%202%5D%5C%5C%3D-m%5E2-4m%5E2%2B6%2B2%2B7m%5C%5C%3D-5m%5E2%2B7m%2B8)
This is the sum of the 2 polynomials shown:
Answer:
Step-by-step explanation:
2x+5y=12
3x+4y=11
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3(2x+5y)=3(12)
-2(3x+4y)=-2(11)
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6x+15y=36
-6x-8y=-22
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7y=14
y=14/7=2
2x+5(2)=12
2x+10=12
2x=12-10=2
x=2/2=1
x=1, y=2. (1, 2)
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I just provided you an example of a system of equations and I already solved it for you.
