Please show me how to solve for: -x+2y=6
you can solve for x or for y.
Which is of interest to you?
x =2(y+3) or y=3+1/2x
To solve for the variables in the equation -x + 2y = 6, you can follow these steps:
Step 1: Isolate one variable
In this equation, let's isolate x. To do that, we can first eliminate the coefficient in front of x by multiplying the entire equation by -1:
(-1)(-x + 2y) = (-1)(6)
This simplifies to:
x - 2y = -6
Step 2: Solve for x
Now, we can solve for x by adding 2y to both sides of the equation:
x - 2y + 2y = -6 + 2y
The -2y and +2y cancel each other out, leaving:
x = 2y - 6
Step 3: Substitute
We have an expression for x in terms of y. We can substitute this expression back into the original equation to solve for y:
-x + 2y = 6
Now, substitute 2y - 6 for x:
-(2y - 6) + 2y = 6
Distribute the negative sign:
-2y + 6 + 2y = 6
Simplify:
6 = 6
Step 4: Interpretation
Since 6 = 6, this equation is an identity. It means that there are infinitely many solutions. Any values of x and y that satisfy the equation -x + 2y = 6 will be a solution.
So, the solution to the equation -x + 2y = 6 is a set of infinitely many solutions.