SOLUTION: solve the following simultaneous equations using elimination method, x+2y+3=6 2x+3y+4+6 -x+y=4

Algebra ->  Equations -> SOLUTION: solve the following simultaneous equations using elimination method, x+2y+3=6 2x+3y+4+6 -x+y=4      Log On


   

Question 1075580: solve the following simultaneous equations using elimination method,
x+2y+3=6
2x+3y+4+6
-x+y=4
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2B2y%2B3=6+ (1)
+2x%2B3y%2B4%2B6-x%2By=4+ (2)
—————————————————————————
First, simplify each:
+x%2B2y+=+3+ (1')
+x%2B4y+=+-6+ (2')
Ordinarily, you'd now multiply one equation by some constant so that either the coefficient of 'x' (or 'y') would match in the two equations, but we already have '1x' in each equation, so we can eliminate x by subtracting (2') from (1'):
+x+-+x+%2B+2y+-+4y+=+3-%28-6%29+
++++++++++++-2y+=+9+
+++y+=+-9%2F2+
Find 'x' using (1') (or (2') if you wish):
x+%2B+2y+=+3+ —> +x+%2B+2%28-9%2F2%29+=+3+ —> +x+=+3+%2B+9+=+12+
—
Ans: x=12 and y=-9%2F2
—
Check using (2'): 12+4(-9/2) = 12 + (-18) = -6 (ok)
Check using (1') (we used (1') to find 'x' so this better check!): 12 + 2(-9/2) = 12 -9 = 3 (ok)