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

Algebra ->  Coordinate Systems and Linear Equations -> 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       Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+=+2
x+=+4y+%2B+5

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.

cartoon%28red%28x%29%2By=2%2Cred%284y%2B5%29%2By=2%29

Now collect terms:
4y%2B5%2By=2

5y%2B5=2

Add -5 to both sides:
5y=2-5
5y=-3

And divide by 5:
y=-3%2F5

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

x%2B%28-3%2F5%29=2

Add 3%2F5 to both sides:
x=2%2B3%2F5
x=10%2F5%2B3%2F5=13%2F5

Therefore, the solution set to this system of equations consists of the single ordered pair (13%2F5,-3%2F5)

Check:
13%2F5%2B%28-3%2F5%29=10%2F5=2
13%2F5=4%28-3%2F5%29%2B5=-12%2F5%2B25%2F5=13%2F5 Answer checks.