Final answer:
The system of linear equations 11x + 4y = -46 and 7x - 4y = 10 is solved using the elimination method, obtaining the solution x = -2 and y = -6.
Step-by-step explanation:
The student's question involves a system of linear equations, which can be solved using various methods such as substitution, elimination, or graphing. Here, the two given equations are:
- 11x + 4y = -46
- 7x - 4y = 10
To solve the system, we can use the elimination method, adding the two equations together to eliminate the y terms:
11x + 4y + 7x - 4y = -46 + 10
This simplifies to:
18x = -36
Dividing both sides by 18 gives us:
x = -2
Substituting x = -2 into one of the original equations to find the value of y:
11(-2) + 4y = -46
Which simplifies to:
-22 + 4y = -46
Adding 22 to both sides gives us:
4y = -24
Dividing by 4 we get:
y = -6
Thus, the solution to the system of equations is x = -2 and y = -6.