SOLUTION: I would love to have some help with solving this system of equations using the substitution method. Thanks! x + y = 2 x = 4y + 5

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Question 133485: I would love to have some help with solving this system of equations using the substitution method. Thanks!


x + y = 2
x = 4y + 5
Found 2 solutions by oscargut, solver91311:
Answer by oscargut(2103)   (Show Source): You can put this solution on YOUR website!
x + y = 2
x = 4y + 5
if you do the substitution of x in the first equation you have:
4y+5+y=2
then
5y=-3
then
y=-3/5
then
x=4(-3/5)+5=(-12/5)+25/5=13/5
then
Answer: x=13/5 and y=-3/5 is the solution
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!



The second equation gives us an expression in terms of y that is equal to x, so we can substitute this expression into the first equation anywhere there is an x.



Now collect terms:




Add -5 to both sides:



And divide by 5:


Now take the first equation again and substitute this newly discovered value for y:



Add to both sides:



Therefore, the solution set to this system of equations consists of the single ordered pair (,)

Check:

Answer checks.
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