Answer:
To solve the given system of equations, we can use either the substitution method or the elimination method. Let’s solve it using the elimination method:
Given equations:
14x + 8y = 20
-7x - 7y = 14
To eliminate one variable, we can multiply equation 2 by -2:
14x + 8y = 20
14x + 14y = -28
Now, subtract equation 2 from equation 1:
(14x + 8y) - (14x + 14y) = 20 - (-28)
14x + 8y - 14x - 14y = 20 + 28
-6y = 48
Divide both sides of the equation by -6:
y = 48 / -6
y = -8
Now, substitute the value of y into one of the original equations, let’s use equation 1:
14x + 8(-8) = 20
14x - 64 = 20
14x = 20 + 64
14x = 84
x = 84 / 14
x = 6
Thus, the solution to the given system of equations is x = 6 and y = -8.
To confirm this solution, you can substitute these values back into both original equations and check if they hold true.