Ask a question

How do I solve a linear system

In Algebra 1 we're working on solving linear systems, to problems like "x=y+3 2x-y+5" And I don't even know where to start.

4 Answers by Expert Tutors

Tutors, sign in to answer this question.
Tom D. | Very patient Math Expert who likes to teachVery patient Math Expert who likes to te...
You'll learn better techniques for higher order systems, but the 2nd order system (2 eqtns with 2 unknowns) is straightforward to solve by hand.  Here are the general steps
1) Place both equations in the form aX + bY = c
2) Inspect the constants of both equations to find a GCM for either X or Y
3) Multiply Either equation (or both) to achieve the GCM in both eqtns for that X or Y
4) Add or subtract the equations to get RID of that X or Y
5) Solve for that remaining Y or X
6) Substitute that first answer (YorX) to compute the other (XorY)
Let's do your example
2)Looking at the above, you'll note that if we subtract the 1st equation from the 2nd, we can make the Y-variable disappear.  To be clear, I'll rewrite them
-( x-y)=3
x = (5-3)=2
6) Now just pick an equation to substitute back to find y (doesn't matter which one you use)
-y=3-x    (moved x to the right on 1st eqtn)
 y=x-3    (multiplied by -1 on both sides)
 y=(2)-3= -1  (substituted 2 into x from above)-----> (x,y)=(2,-1)
6) Lets check the other eqtn just to verify
-y =-2x + 5
y= 2x - 5  (multiplied by -1 on both sides)
y=2(2)-5= -1 (substituted 2 into x from above)-----> (x,y)=(2,-1)  VERIFIED!


did you mean 2x-y=5 for the 2nd eqtn?  If so, this is correct.
Md Akib Ali S. | Tutor Who Can Tutor all Science, Math, and Engineering SubjectsTutor Who Can Tutor all Science, Math, a...
Ok as you have said this is linear equation. The first step is to take "x" and "y" to one side for both the equation so you get: x-y = 3 (subtracting y on both side) and 2x-y = -5 ( subtracting 5 both side). Now you subtract the two equation you get : -x = 8, so x = -8 and putting this "x" in first equation gives -8 - y =3. So y= -11. Thank You
Daniel B. | UM Grad with MA in Mathematics specializes in Algebra (and proofs)UM Grad with MA in Mathematics specializ...
Instead of adding equations you could also just use substitution since we know x=y+3.  Plug in x in the 2nd equation and we get
2(y+3)-y=5            Solve for y.
Now plug in y in the 1st equation and we get
Hope this helps!
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
X = y +3
2X - y = 5
  X - y = 3   (1)
 2X - y = 5  ( 2)                       / first make equations in the standard form of
                                         / aX + b =c
   You see here that if you subtract equation equ  (1) from (2)
  X = 5-3 = 2
   Substitute  X =2 back to equation (1)
       2 - y = 3       Y = 2 - 3 = -1


would I be able to talk live about this, if so you'll need a lot of patience, it will take a bit for me to understand it
There's a small error: the standard form is actually ax + by = c.  You just forgot the 'y'.