system of equations by substitution?

Question

Solve the system of equations by substitution:

4x - 3y = 1
12x - 9y = 3

Answer 1

No solution

The coefficients and variables cancell

- - - - - - - - s-

Answer 2

Hi,

4x - 3y = 1
12x - 9y = 3

Solving 4x - 3y = 1 for x gives x = (1 + 3y)/4. Substituting this into the second equation gives:

12x - 9y = 3
12((1 + 3y)/4) - 9y = 3
3(1 + 3y) - 9y = 3
3 + 9y - 9y = 3
3 = 3

Since the variables all dropped out and gave a statement that is ALWAYS true, that means that this system is true for every point on a line because the 2 equations have the same graph and intersect at an infinite number of points.

So there are an infinite number of solutions.

I hope that helps!! :-)

Answer 3

4x=1+3y-----------------------(1)
also 12x-9y=3or 3(4x)-9y=3
or 3(1+3y)-9y=3------using (1)
or 3+9y-9y=3 or 0=0
so the system of equations doesn't have a solution.

Answer 4

Dude,

This is how you do it.

Solve the first equation for 9y.
Then plug this into the 2nd equation so that your equation is only in terms of x.
Solve for x.
Then solve for y from either equation.

I would be doing you a disservice if I did it for you.