Final answer:
The solution to the system of equations is x = -1 and y = -6.
Step-by-step explanation:
To solve the system of equations:
7x + 7y = -49
7x - 2y = 5
- Multiply the second equation by 7 to make the x terms cancel when added:
- 49x - 14y = 35
- Add the two equations:
- 49x - 14y + 7x + 7y = 35 - 49
- 56x - 7y = -14
- Combine like terms:
- 56x - 7y = -14
- 49x - 14y = 35
- Multiply the first equation by 7 and the second equation by 8:
- 392x - 49y = -98
- 392x - 112y = 280
- Subtract the second equation from the first:
- 392x - 49y - (392x - 112y) = -98 - 280
- 392x - 49y - 392x + 112y = -378
- 63y = -378
- Divide both sides by 63:
- y = -378/63
- y = -6
- Substitute the value of y back into one of the original equations:
- 7x + 7(-6) = -49
- Simplify and solve for x:
- 7x - 42 = -49
- 7x = -7
- x = -1
The solution to the system of equations is x = -1 and y = -6.