1. In the equations provided, the like terms are 6x and -3x. They are related because they both represent the coefficient of x in their respective equations. Similarly, 4y and 5y are like terms because they represent the coefficient of y in their respective equations.
2. To solve the linear system using the substitution method, we can solve one equation for one variable and substitute that expression into the other equation.
From equation (1):
8x + y = -458
=> y = -8x - 458
Substitute the value of y in equation (2):
-5x + 3(-8x - 458) = 221
Simplify:
-5x - 24x - 1374 = 221
Combine like terms:
-29x - 1374 = 221
Add 1374 to both sides:
-29x = 595
Divide by -29:
x = -20.5
Substitute the value of x into equation (1) to find y:
8(-20.5) + y = -458
-164 + y = -458
y = -458 + 164
y = -294
Therefore, the solution to the linear system is x = -20.5 and y = -294.