Question 1030611: Solve the system of equations by using substitution. Express the answer as an ordered pair:
x-5y=2
9x+8=15y
Found 4 solutions by mananth, MathTherapy, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! 1 x + -5 y = 2 .............1
-5 y = 2 + -1 x
/ -5 =
y = - 2/5 + 1/5 x
9 x + -15 y = -8 .....................2
Substitute y in (2)
9 x + -15 ( - 2/5 + 1/5 x ) = -8
9 x + 6 + -3 x = -8
9 x -3 x = -14
6 x = -14
/ 6
x= -2 1/3
Plug the value of x in (1)
1 x + -5 y = 2
1 * -2 1/3 + -5 y = 2
-2 1/3 + -5 y = 2
-5 y = 4 1/3
/ -5
y= - 7/8
m.ananth@hotmail.ca
Answer by MathTherapy(10801)  (Show Source):
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
Solve the system of equations by using substitution. Express the answer as an ordered pair:
x - 5y = 2
9x + 8 = 15y
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solving systems of linear equations is an algorithmic procedure, from one side,
and an art, from the other side - both at the same time. Teaching students to solve
such systems is teaching to algorithmic procedure and teaching to the art, in the same time.
In the given system, the coefficient at 'x' in the first equation equals 1, so it is very natural
to express 'x' from this equation and to substitute this expression into the second equation.
@mananth uses his computer code, which is written in stiff manner and knows nothing about the art of solving.
It only performs one preassigned/programmed procedure, which is not appropriate for this given system of
equations. Therefore, the @mananth' solution is absolutely inappropriate for solving this concrete system
and is inappropriate in degree 2 for TEACHING students on solving this system and other similar systems.
Your starting equations are
x - 5y = 2 (1)
9x + 8 = 15y (2)
From the first equation, express
x = 5y + 2 (3)
and substitute it into the second equation
9(5y+2) + 8 = 15y.
Now simplify it and find y
45y + 18 + 8 = 15y,
45y - 15y = - 26,
30y = -26,
y =  =  .
Now substitute this value of 'y' into (3) and find 'x'
x =  =  =  =  .
ANSWER. The solution of the system is x = , y = .
The final answer in the post by @mananth is  .
Again, the way on how @mananth solves this system, is inappropriate.
His computer code is written in stiff manner; it is not able to adapt to the form of equations
and to find an optimal way of solution. In this form and due to this reason, his code
is inappropriate for using in teaching.
Answer by n2(78)  (Show Source):
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