Question 73446This question is from textbook discovering algebra
: How can we get an answer to Solving systems of equations using elimination, such as the one below
2x+5y=-1
x+2y=0
This question is from textbook discovering algebra
Found 2 solutions by bucky, ankor@dixie-net.com:
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 2x+5y=-1
x+ 2y= 0
.
The method to solve this equation set by elimination is to make a term in one of the equations
equal to a term in the other equation and then subtract the two equations to get rid
of the common term.
.
For this set of equations, the easiest thing to do would be to multiply the bottom equation
by 2 (multiply all terms on both sides). Then both of the equations would contain the
term 2x and if you subtracted the two equations the result would be a single equation
without any terms involving x. This would be solvable. But rather that do it the easy way,
let's try to get rid of the y terms by making them equal in both equations. This requires
you to change both equations, not just one, and is more commonly what you might have to
do.
Again your two equations are:
.
2x+5y=-1
x+ 2y= 0
.
To get rid of the y terms suppose we multiply the top equation by 2 (all terms on both
sides). When we do it becomes:
.
4x + 10y = -2
.
Then suppose we multiply the bottom equation by 5 (same thing: multiply all terms on
both sides). The result is:
.
5x + 10y = 0
.
So the set of equations we are dealing with has now been transformed to:
.
4x + 10y = -2
5x + 10y = 0
.
If we now subtract these two, the terms in the y column will disappear. In the x column
we end up with -x and in the numbers column on the right side we end up with -2. So our
new equation is:
.
-x = -2
.
and multiplying both sides by -1 gives us x = +2
.
We can now take that value back to any of the equations, substitute it, and solve for
y.
.
Let's go back to the original bottom equation:
.
x + 2y = 0
.
Substitute +2 for x to get:
.
+2 + 2y = 0
.
Subtract 2 from both sides to eliminate the +2 on the left side and the equation becomes:
.
2y = -2
.
Finally divide both sides by 2 to find that y = -1
.
So the solution set for this pair of equations is x = 2 and y = -1 or in another way of
looking at it, the graphs of the two equations intersect at the point (2, -1)
.
Hope this gives you a basic insight into solving two linear equations using the method
of elimination.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! ow can we get an answer to Solving systems of equations using elimination, such as the one below
2x + 5y = -1
x + 2y = 0
:
When you use the "elimination method", we multiply 1 or both equations so that
when we add or subtract the two equations, one of the unknowns is eliminated.
:
Multiply the 2nd equation by 2, and subtract from the 1st equation:
2x + 5y = -1
2x + 4y = 0
-------------- subtracting, eliminates x
0x + 1y = -1
:
Therefore we know y = -1
:
Find x by substituting -1 for y in the 1st equation:
2x + 5(-1) = -1
2x - 5 = -1
2x = -1 + 5; added 5 to both sides
2x = +4
x = 4/2; divided both sides by 2
x = 2
:
Check for equality by substituting both solutions in the 2nd equation:
2 + 2(-1) = 0
2 - 2 = 0; proves our solutions are right
:
Do you think you will be able to do this now? Any questions?
|
|
|
