|
Question 1085986: solve by comparison
x+2y =4
x+y=2
another
x-4y=1
x+y=-4
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the comparison method essentially solves each equation for a selected variable and then compares the value of that same variable to each other.
the concept uses the basic mathematical rule of:
if a = b and a = c, then b = c because they are both equal to a.
note that, if you subtract the second equation from the first, you will get:
a = b minus a = c becomes 0 = b - c
add c to both sides of this equation to get c = b which is the same as b = c.
using this concept, you would do the following:
for the first set of equations:
x+2y = 4
x+y=2
solve for x in both equations.
you will get:
x = 4 - 2y
x = 2 - y
since both expressions on the right are equal to x, then set them equal to each other and solve.
you will get:
4 - 2y = 2 - y
add 2y to both sides of the equation and subtract 2 from both sides of the equation to get:
4 - 2 = -y + 2y
combine like terms to get 2 = y
use the value of 2 for y in either original equation to find x.
x+y=2 becomes x + 2 = 2 which becomes x = 0.
your values are x = 0 and y = 2.
both original equations will be true with these value as shown below:
x+2y = 4 becomes 0 + 2*2 = 4 which becomes 4 = 4 which is true.
x + y = 2 becomes 0 + 2 = 2 which becomes 2 = 2 which is true.
-------------------------------------------------------------
in the second set of equations, start with:
x-4y=1
x+y=-4
solve for x in both equations to get:
x = 4y + 1
x = -4 - y
since both expressions on the right side of the equal sign are both equal to x, set them equal to each other to get:
4y + 1 = -4 - y
subtract 1 from both sides of the equation and add y to both sides of the equation to get:
5y = -5
solve for y to get y = -5/5 = -1
replace y with -1 in either original equation to find the value of x.
x-4y=1 becomes x - 4*(-1) = 1 which becomes x + 4 = 1 which becomes x = -3
when x = -3 and y = -1, both original equations should be true.
x-4y=1 becomes -3 - 4 * -1) = 1 which becomes -3 + 4 = 1 which becomes 1 = 1 which it true.
x+y=-4 becomes -3 + (-1) = -4 which becomes -3 - 1 = -4 which becomes -4 = -4 which is true.
both original equations are true, so the solution is good.
here's a reference on the comparison method.
http://study.com/academy/lesson/comparison-method-for-solving-math-problems.html
|
|
|
| |
