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poizon [28]
3 years ago
11

What is the solution to this system of equations? 5X + 2y =29 X + 4y=13

Mathematics
2 answers:
Lorico [155]3 years ago
7 0
5x+2y=29
x+4y=13
eliminate y's

multiply top equation by -2 and add to first

-10x-4y=-58
<u>x+4y=13 +</u>
-9x+0y=-45

-9x=-45
divide  both sides by -9
x=5
sub baack

x+4y=13
5+4y=13
minus 5 both sides
4y=8
divide both sidse by 4
y=2

x=5
y=2
(x,y)
(5,2)


NARA [144]3 years ago
5 0
I hope this helps you

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In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, &amp; KM = 3x + 23, find x &amp; the measure of each angle.
Dennis_Churaev [7]

Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

<u>Step-by-step explanation:</u>

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

 KM ≅ LM

3x + 23 = 7x - 37

       23 = 4x - 37

       60 = 4x

        15 = x

KM = LM = 3x + 23

               = 3(15) + 23

               = 45 + 23

               = 68

KL = 9x - 40

    = 9(15) - 40

    = 135 - 40

    = 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
  • Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = \frac{adjacent}{hypotenuse}

cos ∠L = \frac{47.5}{68}

      ∠L = cos⁻¹ (\frac{47.5}{68})

      ∠L = 45.7  

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

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3 years ago
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