SOLUTION: I need help with four problems. You have to solve each system of equations by substitutions. Te first one i need help with is x+y=1 2x-y=-2. The second one is 5x-3y=-11 and x-2y=2

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I'll do the first two to get you started


# 1




Start with the given system of equations:





Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



---------------------

Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute the negative


Combine like terms on the left side


Add 1 to both sides


Combine like terms on the right side


Divide both sides by 3 to isolate x



Reduce





-----------------First Answer------------------------------


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is:









-----------------Summary------------------------------

So our answers are:

and

which form the point

---

# 2





Start with the given system of equations:





Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



---------------------

Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



Distribute and multiply the LCM to each side



Combine like terms on the left side


Add 22 to both sides


Combine like terms on the right side


Divide both sides by -7 to isolate x



Divide





-----------------First Answer------------------------------


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is:









-----------------Summary------------------------------

So our answers are:

and

which form the point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of (red) and (green) and the intersection of the lines (blue circle).