Final answer:
To solve the system of linear equations, we first simplify the equations and then use subtraction to eliminate one variable. After finding the value of one variable, we substitute it back into one of the original equations to find the value of the other variable. The solution is x = 4 and y = -2.
Step-by-step explanation:
To solve the system of linear equations, we manipulate the equations to isolate the variables. The given system consists of:
- 3x - 4y = x - y + 4
- 2x + 6y = 5y - 4
For the first equation, subtract 'x' and add 'y' to both sides:
2x - 3y = 4
For the second equation, subtract '5y' from both sides to get:
2x + y = -4
Now we have a new system:
Subtract the second equation from the first (to eliminate 'x'):
2x - 3y - (2x + y) = 4 - (-4)
-4y = 8
Divide both sides by '-4' to get:
y = -2
Insert 'y = -2' into the second original equation to solve for 'x':
2x + 6(-2) = -4
2x - 12 = -4
Add '12' to both sides:
2x = 8
Divide both sides by '2':
x = 4
The solution to the system is x = 4 and y = -2.