SOLUTION: Solve each pair of equation given below using elimination method:X+2y=-4. 3x-5y=-1

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Question 1076557: Solve each pair of equation given below using elimination method:X+2y=-4. 3x-5y=-1
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B2y=-4
3x-5y=-1
------------------

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


Lets start with the given system of linear equations

1%2Ax%2B2%2Ay=-4
3%2Ax-5%2Ay=-1

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 1 and 3 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and 3 is 3, we need to multiply both sides of the top equation by 3 and multiply both sides of the bottom equation by -1 like this:

3%2A%281%2Ax%2B2%2Ay%29=%28-4%29%2A3 Multiply the top equation (both sides) by 3
-1%2A%283%2Ax-5%2Ay%29=%28-1%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
3%2Ax%2B6%2Ay=-12
-3%2Ax%2B5%2Ay=1

Notice how 3 and -3 add to zero (ie 3%2B-3=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%283%2Ax-3%2Ax%29%2B%286%2Ay%2B5%2Ay%29=-12%2B1

%283-3%29%2Ax%2B%286%2B5%29y=-12%2B1

cross%283%2B-3%29%2Ax%2B%286%2B5%29%2Ay=-12%2B1 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:

11%2Ay=-11

y=-11%2F11 Divide both sides by 11 to solve for y



y=-1 Reduce


Now plug this answer into the top equation 1%2Ax%2B2%2Ay=-4 to solve for x

1%2Ax%2B2%28-1%29=-4 Plug in y=-1


1%2Ax-2=-4 Multiply



1%2Ax=-4%2B2 Subtract -2 from both sides

1%2Ax=-2 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ax=%28-2%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 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)

1%2Ax%2B2%2Ay=-4
3%2Ax-5%2Ay=-1

we get



graph of 1%2Ax%2B2%2Ay=-4 (red) 3%2Ax-5%2Ay=-1 (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 MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve each pair of equation given below using elimination method:X+2y=-4. 3x-5y=-1
I'm assuming that X is same as x. Do not write X and x as they signify 2 DIFFERENT variables

x + 2y = - 4 ------- eq (i)

3x - 5y = - 1 ------ eq (ii)

- 3x - 6y = 12 ----- Multiplying eq (i) by - 3 ------ eq (iii)

   - 11y = 11 ------ Adding eqs (iii) & (ii)

highlight_green%28matrix%281%2C5%2C+y%2C+%22=%22%2C+11%2F%28-+11%29%2C+%22=%22%2C+-+1%29%29

Substitute - 1 for y into any of the 2 original equations to get the value of x.