| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations 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 2 to some equal number, we could try to get them to the LCM. Since the LCM of 1 and 2 is 2, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this: So after multiplying we get this: Notice how 2 and -2 add to zero (ie Now add the equations together. In order to add 2 equations, group like terms and combine them So after adding and canceling out the x terms we're left with: Now plug this answer into the top equation So our answer is which also looks like ( Notice if we graph the equations (if you need help with graphing, check out this solver) we get and we can see that the two equations intersect at ( |
Your starting equations are
x + 3y = -13 (1)
2x = 3y + 10 (2)
Keep the first equation as is.
In the second equation, move the term 3y from the right side to the left side, changing its sign. You will get
x + 3y = -13 (3)
2x - 3y = 10 (4)
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| Now the system of equations is in its standard form, |
| and we can apply the Elimination method. |
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For it, add equations (3) and (4). The terms "3y" and "-3y" will cancel each other, and you will get the final equation
3x = -3
for one single unknown x. (It is how the elimination method works).
From this last equation, x = -3/3 = -1.
Now substitute the found value x= -1 into either of original equations to get y.
I will substitute it into equation (1)
-1 + 3y = -13
which gives
3y = -13 + 1 = -12,
and then y = -12/3 = -4.
The problem is just solved. The ANSWER is x= -1, y= -4.
You may check the answer by substituting the found values into the original equations.
- Did I say ". . . you may ?" - - - No, I mean " you MUST ".
I leave this check to you.