How do you solve #2x + 3y = 12# and #x + 4y = 11#?

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Answer 1 · 2018-05-28T01:13:28

#x=3, y=2#

Let's start with the second equation and solve for #x# in terms of #y#.

We can subtract #4y# from both sides to get

#color(blue)(x=11-4y)#

We have solved for #x# in terms of #y#, so we can plug this into the first equation. We get

#2(11-4y)+3y=12#

Distributing the #2#, we get

#22-8y+3y=12#

Combining like terms, we get

#22-5y=12#

We can subtract #22# from both sides to get

#-5y=-10#

Dividing both sides by #-5#, we get

#y=2#

To completely solve for #x#, we can go back to the equation I have in blue, and plug in #y=2#. We get

#x=11-4(2)#

#x=11-8#

#x=3#

Thus, #x=3# and #y=2#.

Hope this helps!