To write in slope-intercept form, you first need to get y by itself. To do this, subtract 7x from both sides of the equation.
Doing this gets you: y = 25 - 7x
Now that y is by itself, remember that slope-intercept form looks like this: y = mx + b
So, let's switch the right side.
y = -7x + 25
Slope intercept form is: y = -7x + 25
Rules for y in Slope-Intercept form:
y must be positive
y must be by itself (so, not 2y, or anything with it... just y)
You first have to set up the two equations. Y is equal to the total number of gallons in a tank and x is equal to the number of hours the tanks are filling.
Since the two equations both equal y I can make them equal each other. I then solved for x as you see and got -4.
Once I found my x value I now needed to find my y. You only needed to chose one equation to solve for y, so I decided to do the first one. I plugged in -4 where my x value currently was and solved for y. I got 2.
If you have any questions please comment!! Hope this helps!!
You start by doing 65.20 (the bill) divided by 5 (the amount of people paying)
65.20 / 5 = 13.04
Then you add 13.04 (how much each person paid towards the bill) and 2.75 (the amount of money each person left as a tip)
13.04 + 2.75 = 15.79
Each person paid $15.79
Combine the 2nd and 3rd equations. 3x will disappear:
2y + 5z = 7 This is true for any y and z, and is independent of x.
7-5z
Solving for y, 2y = 7 - 5z, so that y = ---------
2
We have to eliminate x again by using the 1st and 2nd equations:
-2x - 6y - 2z = -2. We want the coeff. of x in the first eqn to be -3.
Therefore, mult. all terms of -2x - 6y - 2z = -2 by 3/2:
(3/2)(-2x - 6y - 2z = -2) = -3x -9y -3z =-3
Now add this version of the 1st row to the 2nd row:
-3x -9y -3z =-3
3x +2y +5z = 7
----------------------
-7y + 2z = 4
7 - 5z
We found earlier that y = ----------, and can elim. y by subst. this fraction into
2
-7y + 2z = 4. Then -7y + 2z = 4 becomes -7( (7-5z)/2 ) + 2Z = 4.
Elim. the fraction by mult. all terms by 2:
-7(7-5z) + 4z = 8 which becomes -49 + 35z + 4z = 8
so that 39z = 57, and so z = 57/39.
Subst. this back into -7y + 2z = 4 to calculate y. Make a final subst. to calculate x.
Given the choice, I would solve this system using matrices.
Turns out that the solution, using matrices, does not exist.
