Question #2077b

1 Answer
Y
May 16, 2017

Answer: #(7/2,1)#

Explanation:

Solve:
#2x+3y=10#
#5x+2y=19.5#

We can solve this system of equations by elimination.
First, we need to multiply the first equation by #5# and the second equation by #2# to make the #x# coefficient same for both equations:
#5(2x+3y=10)#
#10x+15y=50#

#2(5x+2y=19.5)#
#10x+4y=39#

Since the #x# coefficient for both equations is now #10#, we can subtract the second equation from the first equation and simplify:
#10x+15y-(10x+4y)=50-39#
#10x+15y-10x-4y=11#
#11y=11#
#y=1#

Now, we can substitute this #y# value into one of the original equations and solve for #x#, we'll use the first one:
#2x+3(1)=10#
#2x+3=10#
#2x=7#
#x=7/2#

Therefore, our answer as a coordinate is #(7/2,1)#

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