SOLUTION: Using the Substitution Method, solve the system 2x + 3y = -4 x - 2y = 5

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Question 190104: Using the Substitution Method, solve the system
2x + 3y = -4
x - 2y = 5

Answer by cutepiscean5(19) About Me  (Show Source):
You can put this solution on YOUR website!
we have the given equations as :
+2x+%2B+3y+=+-4+ ........ (1)
+x+-+2y+=+5+ ............(2)
from equation (2) we extract x in terms of y and we get:
+x+-+2y+=+5+
Now, add 2y to both sides of the equation, such that 2y on the left hand side cancels out.
=> +x+-+cross%282y%29+%2B+cross%282y%29+=+2y+%2B+5+
=> +x+=+2y+%2B+5+ ............(3)
substitute , this value of x into the first equation (1) . we get:
+2x+%2B+3y+=+-4+
=> +2%282y+%2B+5%29+%2B+3y+=+-4+ (use distributive law to open the brackets)
=> +4y+%2B+10+%2B+3y+=+-4+ (now, combine the like terms)
=> +7y+%2B+10+=+-4+ (Subtract 10 from both sides)
=> +7y+=+-4+-+10+
=> +7y+=+-14+
=> +y+=+-14%2F7+
=> +highlight%28y+=+-2%29+
now plug in this value of y, into the equation (3) to get the value of x,
=> +x+=+2y+%2B+5+
=> +x+=+2%28-2%29+%2B+5+
=> +x+=+-4+%2B+5+
=> +highlight%28x+=+1%29+
Checking plug in values of x and y in both equations and verify:
In Equation (1)
+2x+%2B+3y+=+-4+
=> +2%281%29+%2B+3%28-2%29+=+-4+
=> +2+-+6+=+-4+
=> +-4+=+-4+, which is true.
In Equation (2)
+x+-+2y+=+5+
=> +%281%29+-+2%28-2%29+=+5+
=> +1+-+%28-4%29+=+5+
=> +1+%2B+4+=+5+
=> +5+=+5+, which is again true,
Hence our answers are correct !
Hope this helps.