What are x and y if #5x - 2y = -5# and #y - 5x = 3#?

Answer 1

#color(brown)(x = -1/5, y = 2#

#5 x - 2 y = -5, " Eqn (1)"#
#y - 5 x = 3, " Eqn (2)"#
#y = 5x + 3#

Substituting value of y in terms of x in Eqn (1)"#,

#5x - 2*(5x + 3) = -5#
#5x - 10x - 6 = -5#
#-5x = -1, x = -1/5#
#y = 5x + 3 = 5 * (-1/5) + 3 = 2#
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Answer 2

The solution is #(-1/5,2)# or #(-0.2,2)#.

We can also use elimination to solve this system of linear equations.

#"Equation 1":# #5x-2y=-5#
#"Equation 2":# #y-5x=3#

Rewrite Equation 2:

#-5x+y=3#

Add: Equation 1 + Equation 2:

#-5x + color(white)(.)y =color(white)(....)3# #ul(color(white)(..)5x-2y=-5)# #color(white)(........)-y=-2#
Divide both sides by #-1#. This will reverse the signs.
#y=2#
Substitute #2# for #y# in Equation 2 (either equation will work).
#2-5x=3#
Subtract #2# from both sides.
#-5x=3-2#
#-5x=1#
Divide both sides by #-5#.
#x=-1/5#
The solution is #(-1/5,2)# or #(-0.2,2)#.

graph{(5x-2y+5)(y-5x-3)=0 [-10, 10, -5, 5]}

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Answer 3

x = 1, y = -2

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Answer 4

To find the values of x and y, you can solve the given system of equations simultaneously.

  1. Start with the first equation: 5x - 2y = -5

  2. Solve for y: y = (5x + 5) / 2

  3. Substitute this expression for y into the second equation: (5x + 5) / 2 - 5x = 3

  4. Simplify and solve for x: x = -4

  5. Once you have the value of x, substitute it back into either of the original equations to find y. Using the first equation: 5(-4) - 2y = -5 -20 - 2y = -5 -2y = 15 y = -7.5

Therefore, the solution is x = -4 and y = -7.5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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