solve using addition or subtration
12x+9y= 14
6x= 7y - 16
To solve the system of equations using addition or subtraction, we need to manipulate one or both equations so that when they are added or subtracted, one of the variables cancels out. Let's solve the system step by step:
Equation 1: 12x + 9y = 14
Equation 2: 6x = 7y - 16
Let's manipulate Equation 2 to make it easier to eliminate one of the variables:
Multiply Equation 2 by 2:
12x = 14y - 32
Now we have:
Equation 1: 12x + 9y = 14
Equation 2: 12x = 14y - 32
Now, we can subtract Equation 2 from Equation 1:
(12x + 9y) - (12x) = 14 - (14y - 32)
Simplifying, we get:
12x - 12x + 9y = 14 - 14y + 32
9y = -14y + 46
Now, we can combine like terms:
23y = 46
Dividing both sides by 23, we find:
y = 2
Now, substitute the value of y back into either equation. Let's use Equation 2:
6x = 7(2) - 16
Simplifying, we get:
6x = 14 - 16
6x = -2
Dividing both sides by 6, we find:
x = -1/3
So the solution to the system of equations is x = -1/3 and y = 2.