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
2u + 7v = 3
3u - 5v = -11
2u + 7v = 3
6u - 10v = -22
6u + 21v = 9
31v = 31
v = 1
so, u = -2
Please help me
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.