Final answer:
To solve the system of equations {-2x-5y= -16, x= -6y+29} by substitution, substitute the value of x into the first equation and solve for y. Then, substitute the value of y back into the second equation to solve for x. The solution is x = -7 and y = 6.
Step-by-step explanation:
To solve the system of equations {-2x-5y= -16, x= -6y+29} by substitution, we can substitute the value of x from the second equation into the first equation.
Using the second equation, we have x = -6y + 29. Substituting this into the first equation, we get: -2(-6y + 29) - 5y = -16.
Simplifying the equation, we get: 12y - 58 - 5y = -16. Combining like terms, we get: 7y = 42. Dividing both sides by 7, we find that y = 6. Substituting this value back into the second equation, we can solve for x: x = -6(6) + 29. Simplifying, we get x = -36 + 29 = -7.
Therefore, the solution to the system of equations {-2x-5y= -16, x= -6y+29} when solving by substitution is x = -7 and y = 6.