1x+3y = 12 Solve for both, show work
x=12-3y
> sub back to 1x+3y=12
1(12-3y)=12
y = 12-3y=12
y = -3y=0
y = 0
>sub y=0 back into 1x+3y=12
1x+0+12
x = 12
answer = x=12, y=0
a single equation with two unknowns has no unique solution
... the values of the variables are interrelated
the solution is a line
in slope-intercept form ... y = -1/3 x + 4
To solve the given equation 1x + 3y = 12, we need to isolate one of the variables on either side of the equation. Let's solve for x by getting rid of the y term.
Step 1: Start with the equation 1x + 3y = 12.
Step 2: Subtract 3y from both sides of the equation to move the term involving y to the other side:
1x + 3y - 3y = 12 - 3y.
Simplifying,
1x = 12 - 3y.
Step 3: The equation now is x = 12 - 3y.
So, the solution to the equation is x = 12 - 3y.
To find the solution for y, we can follow a similar process but solve for y instead of x.
Step 1: Start with the equation 1x + 3y = 12.
Step 2: Subtract x from both sides of the equation to move the term involving x to the other side:
1x - x + 3y = 12 - x.
Simplifying,
3y = 12 - x.
Step 3: Divide both sides of the equation by 3 to isolate y:
(3y)/3 = (12 - x)/3.
Simplifying,
y = (12 - x)/3.
So, the solution to the equation is y = (12 - x)/3.
Therefore, the solutions to the equation are given by the expressions x = 12 - 3y and y = (12 - x)/3.