What is the system of the following linear system?
5x-6y= -10
-15x+14y=10
A. (-5,-8)
B. (-2,0)
C.(4,5)
D. (10,10)
Can you please show your work and explain to me how you got it please I really want to get it. Thanks.
2007-02-07 14:45:29 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
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2007-02-07 14:57:37 · update #1
5x-6y= -10 (i)
-15x+14y=10 (ii)
Multiply (i) by 3 & add to (ii):
15x - 18y = -30 3(i)
-15x + 14y = 10 (ii)
---------------------
-4y = -20
y = 5.
Substitute y= 5 in (i) & solve for x:
5x - 6(5) = -10
5x = 20
x = 4.
The solution for the system is (4,5).
2007-02-07 14:53:47 · answer #1 · answered by S. B. 6 · 2⤊ 0⤋
What you have here are simultaneous linear equations, and your goal is to find the point on the graph at which the two lines will intersect. That point will be the x and y solutions that work for both equations at the same time.
There is more than one method to solving simultaneous equations. I'm going to use the addition method.
You first want to isolate the y variable by eliminating the x variable as follows:
Multiply the first equation by 3 so the x terms in the two equations will cancel out one another:
15x - 18y = -30
Add the second equation to the first equation:
-15x + 14y = 10
Sum:
0x - 4y = -20
Solve for y:
y = 5
Based on the choices you are given, the only possible answer is c. Make sure by plugging the values into each equation.
5(4) - 6(5) = -10 Correct
-15(4) + 14(5) = 10 Correct
When you plot the two linear equations, they will intersect at the point (4,5).
2007-02-07 23:07:47 · answer #2 · answered by dragonwych 5 · 0⤊ 0⤋
Okay, when you're given two equations you need to either graph them (non-exact) or substitute (exact) or elimiate (exact).
By elimination:
5x - 6y = -10
-15x + 14y = 10
3 (5x - 6y) = 3 (-10)
15x -18y = -30
-15x + 14y = 10
15x - 18y = -30<<<<<<<< now you have to add the equations!
-15x + 15x + 14y - 18y = 10 -30
-4y = -20
y = 5<<<<<<< half of the answer!
5x - 6(5) = -10
5x - 30 = -10
5x = 20
x = 4
The answer= (4, 5), so C
2007-02-07 22:53:59 · answer #3 · answered by quarters 2 · 2⤊ 0⤋
you first must get rid of one of the variables by multiplying one equation by a certain number:
3(5x-6y)=(-10)3
-15x+14y=10
so you get
15x-18y=-30
-15x+14y=10
do your addition and subtraction (there will be no more x so you can solve for y)
-4y=-20
divide both sides by -4
y=5 (the negatives cancel eachother out)
now plug 5 in for y in your simplest equation to get x
5x-30=-10
add 30 to both sides
5x=20
divide both sides by 5
you get x=4
so your system would be (4,5) answer C.
hope that was a good explanation
2007-02-07 22:54:09 · answer #4 · answered by schs_spartan 3 · 2⤊ 0⤋
this is really simple plug in the numbers
answer is c, not d.
5(4) - 6(5) = -10
20 - 30 = -10
-15(4) + 14(5) = 10
-60 + 70 = 10
There you go.
2007-02-07 22:54:56 · answer #5 · answered by Genius 4 · 1⤊ 0⤋
Plug in the numbers for x and y, and when they both equal, you have your answer.
20 - 30 = -10
-60 + 70 = 10
Therefore, C is the answer.
2007-02-07 22:54:03 · answer #6 · answered by Anonymous · 1⤊ 0⤋
d
just plug in the numbers
5(10)-6(10)=-10
50-60=-10
-15(10)+14(10)=-10
-150+140=-10
2007-02-07 22:48:05 · answer #7 · answered by Ruth Less RN 5 · 1⤊ 1⤋
the answer is c
just plug the corresponding numbers into the equation and see if they work.
C) is the only one that works on both equations.
2007-02-07 22:53:54 · answer #8 · answered by fade_this_rally 7 · 1⤊ 0⤋