SOLUTION: Please help with this question--What is the x co-ordinate of the system of equations ? 2x + y = 3 and x - 2y = 4. Thanking you Gloria

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help with this question--What is the x co-ordinate of the system of equations ? 2x + y = 3 and x - 2y = 4. Thanking you Gloria      Log On


   

Question 118723: Please help with this question--What is the x co-ordinate of the system of equations ? 2x + y = 3 and x - 2y = 4.
Thanking you
Gloria
Found 2 solutions by MathLover1, m.hansen:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

2%2Ax%2B1%2Ay=3
1%2Ax-2%2Ay=4

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 1 to some equal number, we could try to get them to the LCM.

Since the LCM of 2 and 1 is 2, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -2 like this:

1%2A%282%2Ax%2B1%2Ay%29=%283%29%2A1 Multiply the top equation (both sides) by 1
-2%2A%281%2Ax-2%2Ay%29=%284%29%2A-2 Multiply the bottom equation (both sides) by -2


So after multiplying we get this:
2%2Ax%2B1%2Ay=3
-2%2Ax%2B4%2Ay=-8

Notice how 2 and -2 add to zero (ie 2%2B-2=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%282%2Ax-2%2Ax%29%2B%281%2Ay%2B4%2Ay%29=3-8

%282-2%29%2Ax%2B%281%2B4%29y=3-8

cross%282%2B-2%29%2Ax%2B%281%2B4%29%2Ay=3-8 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.



So after adding and canceling out the x terms we're left with:

5%2Ay=-5

y=-5%2F5 Divide both sides by 5 to solve for y



y=-1 Reduce


Now plug this answer into the top equation 2%2Ax%2B1%2Ay=3 to solve for x

2%2Ax%2B1%28-1%29=3 Plug in y=-1


2%2Ax-1=3 Multiply



2%2Ax=3%2B1 Subtract -1 from both sides

2%2Ax=4 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ax=%284%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.


x=2 Multiply the terms on the right side


So our answer is

x=2, y=-1

which also looks like

(2, -1)

Notice if we graph the equations (if you need help with graphing, check out this solver)

2%2Ax%2B1%2Ay=3
1%2Ax-2%2Ay=4

we get



graph of 2%2Ax%2B1%2Ay=3 (red) 1%2Ax-2%2Ay=4 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).


and we can see that the two equations intersect at (2,-1). This verifies our answer.

Answer by m.hansen(16) About Me  (Show Source):
You can put this solution on YOUR website!
2x + y = 3
x - 2y = 4
:: if we want the x coordinate, we have to get rid of the y
:: if we multiply the top equation by 2, the y becomes 2y,
:: which will cancel the -2y in the second equation
top equ * 2:
4x + 2y = 6
:: now the new top equation and the original bottom equation
4x + 2y = 6
x - 2y = 4
:: add these two equations
5x + 0 = 10
5x = 10
:: divide both sides by 5
x = 2