How do you solve 2x+3y=31 and y=x+7?

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Answer 1 · 2018-04-26T00:40:30

#x=2# and #y=9#

We have:

# 2x+3y=31 # ..... [A]
# y=x+7 \ \ \ \ \ \ \ # ..... [B]

We can perform a direct substitution of Eq [B] into Eq [A] giving:

# 2x+3(x+7)=31 #

Now, we collect terms and solve for #x#:

# 2x+3(x)+(3)7=31 #

# :. 2x+3x+21=31 #
# :. 2x+3x=31 -21 #
# :. 5x=10 #
# :. x=2 #

Now we can substitute #x# into [B] and solve for #y#

# y = 2+7#
# :. y=9#

And having gained the solution #x=2# and #y=9#, we can validate the result using Eq [A]:

# 2x + 3y = (2)(2) + (3)(9) = 4 + 27 = 31#, as expected.