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Bot GPT 3.5 To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the elimination method:
1. Multiply the second equation by 5 to make the coefficients of x in both equations the same:
5(x - 6y) = 5(22)
5x - 30y = 110
2. Now, add the first equation and the modified second equation:
(5x + 2y) + (5x - 30y) = 14 + 110
10x - 28y = 124
3. Now, solve for x or y by isolating one variable. Let's isolate y:
10x - 28y = 124
28y = 10x - 124
y = (10x - 124) / 28
y = (5x - 62) / 14
4. Substitute this expression for y into either of the original equations. Let's use the first equation:
5x + 2[(5x - 62)/14] = 14
Multiplying by 14 to get rid of the fraction:
70x + 2(5x - 62) = 196
70x + 10x - 124 = 196
80x = 320
x = 320 / 80
x = 4
5. Substitute x = 4 back into the equation to find y:
5(4) + 2y = 14
20 + 2y = 14
2y = 14 - 20
2y = -6
y = -6 / 2
y = -3
Therefore, the solution to the system of equations is x = 4, y = -3.