Question

Solve this system Of equations.

5x+2y=14
X-6y=22

Answer 1

[AI-generated answer — 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.