iDENTIFY THE SOLUTION OF THE SYSTEM OF EQUATIONS X + 4Y = 6 4X - 12Y = 3

Question

Identify the solution(s) of the system of equations. -6y - 6y = 24 24y = -24x - 24

 

Answer 1

There are a couple of ways to solve this, but I prefer the elimination method on these types of problems...  A lot of people like substitution.  The truth is substitution is a concept that will probably help you more in later math, but it presents you with a little more complex calculation on this type of problem where errors can occur, you get more fractions, etc...

 

So, anyhoo elimination is easiest when the x and y are on the same side of the equal side and you can multiply one of the equations so you have the same coefficient (number in front of the variable) with opposite signs.  Ie., 3x and -3x or 5y and -5y.  

 

In this case I would like to multiply the first equation by 3.

 

3 (x + 4y) = 6 (3)      becomes 3x + 12y = 18

then add the second equation    4x - 12y = 3

 

Note that the 12y and -12y when added together combine to be 0.  So you yave 7x = 21 and x = 3.  Next take the x value and substitute it back into any one of the original equations.  SO, (3) + 4y = 6,  4y = 3,  y = 3/4

 

You would then write the answer as a coordinate  (3, 3/4) as this point represents the location that the two lines intersect....

 

****When solving systems you must always write the answer in coordinate form and you must have BOTH an x and y value unless you are looking at the same line (infinitely many solutions) or parallel lines (no solution)....