Use Elimination Method To Solve This Simultaneous Equation 5V=11+3U

5v = 11 + 3u

2u + 7v = 3

3u - 5v = -11
2u + 7v = 3

6u - 10v = -22
6u + 21v = 9

31v = 31
v = 1
so, u = -2

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To solve this system of equations using the elimination method, follow these steps:

Step 1: Multiply the first equation by 2 to make the coefficient of U in both equations the same:
2(5V) = 2(11 + 3U)
10V = 22 + 6U

Step 2: Multiply the second equation by 5 to make the coefficient of U in both equations the same:
5(2U + 7V) = 5(3)
10U + 35V = 15

Now you have two equations with the same coefficient for U:

10V = 22 + 6U (equation 1)
10U + 35V = 15 (equation 2)

Step 3: Rearrange equation 1 and equation 2 so that the terms are aligned vertically:

10V - 6U = 22 (equation 1)
10U + 35V = 15 (equation 2)

Step 4: Multiply equation 1 by 5 and equation 2 by 2 to make the coefficients of V in both equations the same:

5(10V - 6U) = 5(22)
2(10U + 35V) = 2(15)

50V - 30U = 110 (equation 3)
20U + 70V = 30 (equation 4)

Step 5: Add equation 3 and equation 4 to eliminate U:
(50V - 30U) + (20U + 70V) = 110 + 30

50V + 70V - 30U + 20U = 140

120V - 10U = 140 (equation 5)

Step 6: Multiply equation 5 by 3 to make the coefficients of U positive and the same as equation 1:

3(120V - 10U) = 3(140)

360V - 30U = 420 (equation 6)

Step 7: Subtract equation 6 from equation 3 to eliminate U:

(50V - 30U) - (360V - 30U) = 110 - 420

50V - 30U - 360V + 30U = -310

-310V = -310

Step 8: Divide both sides of equation 7 by -310 to solve for V:

V = -310 / -310

V = 1

Step 9: Substitute the value of V back into equation 1 or equation 2 to solve for U:

10(1) - 6U = 22

10 - 6U = 22

-6U = 22 - 10

-6U = 12

U = 12 / -6

U = -2

So the solution to the system of equations is U = -2 and V = 1.