Final answer:
To solve the linear equations using the method of linear combination, multiply the equations by appropriate constants to make the coefficients of one variable the same. Then, add the equations to eliminate that variable. Substitute the value of the eliminated variable into one of the original equations to solve for the remaining variable.
Step-by-step explanation:
To solve the equations using linear combination, we can eliminate one variable by multiplying the equations by appropriate constants so that the coefficients of one variable become opposites. We can then add the equations to eliminate that variable. Let's demonstrate:
Multiply the first equation by 10 and the second equation by 2 to make the x-coefficients the same:
20x + 50y = -220
20x + 6y = 44
Subtract the second equation from the first:
(20x + 50y) - (20x + 6y) = -220 - 44
44y = -264
Divide both sides by 44:
y = -6
Now substitute the value of y into one of the original equations:
2x + 5(-6) = -22
2x - 30 = -22
Add 30 to both sides:
2x = 8
Divide both sides by 2:
x = 4
Therefore, the solution to the equations is x = 4 and y = -6.