1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nutka1998 [239]
3 years ago
8

determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y

​

Mathematics
1 answer:
grandymaker [24]3 years ago
7 0

Answer:

  1. (x, y) = (3, 5)
  2. (x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

__

The usual methods of solving a system of equations involve <em>elimination</em> or <em>substitution</em>.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to <em>elimination</em>. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

_____

1. In standard form, your equations are ...

  • 2x -3y = -9
  • 5x +2y = 25

Then the solution is ...

  x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)

__

2. In standard form, your equations are ...

  • 3x +2y = 7
  • 2x +5y = 12

Then the solution is ...

  x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)

_____

<em>Note on Cramer's Rule</em>

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

You might be interested in
can anyone's please explain how you got this answer with explanation....(if nonsense answers I will report)​
solong [7]

Answer:

12.5%

Step-by-step explanation:

45/360×100=12.5

8 0
2 years ago
Ik it seems easy but can someone help
White raven [17]
What are you suppose to find i feel like it doesn't really say
5 0
3 years ago
Given that f(x) = x2 + 3x + 6 and g(x) = the quantity of x plus two, over three, solve for f(g(x)) when x = 1
MaRussiya [10]
Easy
f(g(1))
evaluate g(1) then plug thatin for x in f(x)
g(1)=(x+2)/3
g(1)=(1+2)/3
g(1)=1

f(g(1))=
f(1)=(1)^2+3(1)+6
f(1)=1+3+6
f(1)=10
f(g(1))=10
3 0
3 years ago
Read 2 more answers
Please solve for both it’s due tomorrow, easy points !
PSYCHO15rus [73]

Answer:

13. 0.145, 0.18, 0.206, 0.315

14. 1.75 times

<u><em>WARNING</em></u>

<em>im not completely sure sooo, Im really really sorry if you get it wrong</em>

8 0
3 years ago
Please help if u can
wolverine [178]

Answer:

f(x) -> 2 as x -> -∞ and f(x) -> ∞ as x -> ∞

Step-by-step explanation:

f(x) -> 2 as x -> -∞ and f(x) -> ∞ as x -> ∞

*this is because the graph shows that the y value cannot pass by 2 as the x value constantly decreases and as x is increasing, there is just an arrow showing that the graph is constantly going up and therefore going to ∞

6 0
2 years ago
Other questions:
  • How many lines of symmetry are there in an equilateral triangle?
    5·1 answer
  • Find how much money will be in the account after the given number of years. (Assume 360 days in a year) &amp; his interest
    13·2 answers
  • Which rule describes the transformation that is
    12·1 answer
  • Which equation is a point slope form equation for line AB ?
    10·2 answers
  • the derivative of a sum of two functions is different than the sum of the derivatives of thw two functions?​
    8·1 answer
  • PLEASE ANSWER ASAP<br> expand and simplify the following:<br> a) (√6+√3)(√6-√3) b)(√5-√2)(√2+√5)
    6·2 answers
  • The solution set for -18 &lt; 5x - 3 is _____. -3 &lt; x 3 &lt; x -3 &gt; x 3 &gt; x
    6·2 answers
  • Been trying to figure this out and cant seem to get the answers on the list​
    11·1 answer
  • HEEEELPPPPPP
    11·1 answer
  • noteooks come in four colors red, blue, green, and purple they also come in 2 sizes five subject and 3 subject how many possible
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!