How do you solve 2x-3y=8 and x+y=11 using substitution?

system of equations using substitution. please help I've been stuck on this lesson for weeks.

3 Answers
Feb 21, 2018

Answer:

#x=8.2#, #y=14/5#

Explanation:

Our equations are as follows:
#2x-3y=8#
#x+y=11#

Since the second equation is much simpler, we can subtract #y# from both sides to get an value for #x# in terms of #y#.

Subtracting #y# from both sides of the second equation, we get:

#x=11-y#

We can now substitute this into the first equation:
#2(11-y)-3y=8#, which simplifies to:

#22-2y-3y=8#, which can be simplified more to:

#22-5y=8#

We can solve for #y# now, by subtracting #22# from both sides and dividing both sides by #-5.# We get:

#-5y=-14#

#y=14/5#

We can plug this into either equation to solve for #x.# Let's plug in #14/5# in the first equation, #2x-3y=8#:

#2x-3(14/5)=8#

#2x-42/5=8# (We can change 2x to #10/5x# and 8 into #40/5# to have a common denominator).

#10/5x-42/5=40/5#

Let's add #42/5# to both sides:

#10/5x=82/5#

We can multiply both sides by the reciprocal of #10/5# to solve for #x#.

#x=82/5(5/10)#

The #5s# cancel, and we're left with #82/10# or #x=8.2.#

Feb 21, 2018

Answer:

#x=41/5# and #y=14/5#

Explanation:

#2x-3y=8#
#x+y=11#

We need to solve #x+y=11# for #x#

#x+y=11#

Subtract #y# from both sides

#x+y-y=11-y#

#x=11-y#

now substitute #-y+11# for #x# in #2x -3y=8#

#2x - 3y =8#

#2(-y+11)-3y=8#

Use the distributive property

#(2)(-y)+(2)(11)-3y=8#

#-2y + 22 - 3y =8#

#-5y + 22 = 8#

#-5y = 8-22#

#-5y= -14

Divide both sides by #-5#

#(-5y)/-5=(-14)/-5#

#y= 14/5#

Now substitute #14/5# for #y# in #x=-y+11#

#x=-y+11#

#x=-14/5+11#

#x=(-14)/5 + 11/1#

#x=(-14)/5+11/5#

#x=(-14+55)/5#

#x=41/5#

Answer: #x=41/5# and y#14/5#

Answer:

#(x,y)=(41/5, 14/5) = (8.2, 2.8)#

Explanation:

Isolate #y# in the second equation by subtracting #x# on both sides:

#x+y=11 => y=11-x#

Substitute #y# in the first equation with the expression #11-x# then solve for #x#, then solve for #y#:

#2x - 3y = 8#

#2x - 3(11-x) = 8#

#2x - 33 + 3x = 8#

#5x - 33 = 8#

#5x = 41#

#x = 41/5#

#x = 8.2#

So

#=> y = 11 - (41/5)#

# y = 55/5 - 41/5#

# y = 14/5#

Or

#y = 11 - (8.2)#

# y = 2.8#

Check your solution: insert your values in each of the given equations and verify that they satisfy the system:

#2(8.2) - 3(2.8) = 8 " " {"true"}#

#(8.2) + (2.8) = 11 " "{"true"}#

Your solution is correct.