solve by elimination x+6y-12
-x+7y=1
typo
To solve the system of equations using the elimination method, we need to eliminate one variable. Let's eliminate the variable "x" by adding the two equations together.
The given equations are:
1) x + 6y - 12 = 0
2) -x + 7y = 1
To eliminate "x", we can add equation 1) and equation 2). Adding the left sides and right sides separately, we have:
(x + 6y - 12) + (-x + 7y) = 0 + 1
Simplifying the left side of the equation, we get:
x + 6y - 12 - x + 7y = 1
The "x" term cancels out, giving us:
13y - 12 = 1
Now, let's isolate the "y" variable. We can start by adding 12 to both sides of the equation:
13y - 12 + 12 = 1 + 12
13y = 13
Next, divide both sides of the equation by 13 to solve for "y":
(13y) / 13 = 13 / 13
y = 1
Now that we've found the value of "y" as 1, let's substitute this into one of the original equations to solve for "x". Let's choose equation 2):
-x + 7y = 1
Plugging in y = 1, we have:
-x + 7(1) = 1
-x + 7 = 1
Next, let's isolate the "x" variable. Subtract 7 from both sides of the equation:
-x + 7 - 7 = 1 - 7
-x = -6
To solve for "x", multiply both sides of the equation by -1:
(-1)(-x) = (-1)(-6)
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.