Final answer:
To solve the given system of linear equations, the elimination method is used, resulting in the solution x = 63/26 and y = -97/26.
Step-by-step explanation:
The system of equations presented by the student:
-4x + 5y = 8
6x - y = 11
belongs to the topic of algebra, specifically to solving systems of linear equations. To find the values of x and y that satisfy both equations, we can use methods like substitution or elimination. Let's use elimination in this case:
Multiply the second equation by 5 so that the y terms will cancel out when we add the two equations together. The second equation becomes 30x - 5y = 55.
Add the modified second equation to the first equation:
-4x + 5y = 8
+ 30x - 5y = 55
____________________
26x = 63
Solving for x, we find that x = 63/26.
Substitute x into one of the original equations to find y.
Using 6x - y = 11:
6(63/26) - y = 11
378/26 - y = 11
y = 378/26 - 286/26
y = 92/26
Therefore, the solution to the system of equations is x = 63/26 and y = 92/26.