5v=11+3u
2u+7v=3
Solve with elimination method
from the first
3u - 5v = -11
double this
6u - 10v = -22
triple the 2ns
6u + 21v = 9
.... subtract
32v = 31
v = 1
sub back into 2u+7v=3
2u + 7 = 3
2u = -4
u = -2
as was expected, the AI got it wrong
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply the first equation by 2.
2 * (5v = 11 + 3u) yields 10v = 22 + 6u.
Step 2: Multiply the second equation by 5.
5 * (2u + 7v = 3) yields 10u + 35v = 15.
Step 3: Rearrange the equations to align the coefficients.
Rearrange the equations to be:
10v − 6u = 22
10u + 35v = 15
Step 4: Add the two equations.
Add the left sides and right sides of the equations separately:
(10v − 6u) + (10u + 35v) = 22 + 15
10v + 35v − 6u + 10u = 37.
This simplifies to:
45v + 4u = 37.
Step 5: Rearrange the equation.
Rearrange the equation to be in the form "variable = value":
45v = 37 − 4u.
Step 6: Substitute the new equation into the first equation.
Substitute the value of 45v from the rearranged equation into the first equation:
5v = 11 + 3u.
Replace 45v with (37 − 4u) in the first equation:
5(37 − 4u) = 11 + 3u.
Step 7: Simplify and solve for u.
Distribute 5 to both terms inside the parentheses:
185 − 20u = 11 + 3u.
Combine like terms by subtracting 3u from both sides and subtracting 11 from both sides:
185 − 20u − 3u = 11 + 3u − 3u,
185 − 23u = 11.
Isolate the variable u by subtracting 185 from both sides:
−23u = 11 − 185,
−23u = −174.
Finally, solve for u by dividing both sides by -23:
u = (-174) / (-23),
u = 6.
Step 8: Substitute the value of u into the first equation to solve for v.
Substitute the value of u (6) into the first equation:
5v = 11 + 3u,
5v = 11 + 3(6),
5v = 11 + 18,
5v = 29.
Finally, solve for v by dividing both sides by 5:
v = 29 / 5,
v = 5.8.
Therefore, the solution to the system of equations is u = 6 and v = 5.8.
Subtract 2u from both sides:
7v = 3 - 2u
Substitute 7v for 3 - 2u in the first equation:
5v = 11 + 3u
7v = 3 - 2u
Multiply both sides of the first equation by 7:
35v = 77 + 21u
Subtract 35v from both sides:
77 + 21u - 35v = 0
Substitute 7v for 3 - 2u in the second equation:
77 + 21u - 35(3 - 2u) = 0
Simplify:
77 + 21u - 105 + 70u = 0
Combine like terms:
77 - 35 + 91u = 0
Subtract 77 from both sides:
-35 + 91u = -77
Divide both sides by 91:
u = -77/91
2x-5y=-6
4x-3y=-12
Use elimination method