SOLUTION: Thanks! In which line is a mistake first made when solving the following system of equations by substitution? 3x + y = 9 -2x + y = 4 Line 1 y = -3x + 9 -2x + y = 4 L

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Thanks! In which line is a mistake first made when solving the following system of equations by substitution? 3x + y = 9 -2x + y = 4 Line 1 y = -3x + 9 -2x + y = 4 L      Log On


   

Question 1015007: Thanks!
In which line is a mistake first made when solving the following system of equations by substitution?
3x + y = 9
-2x + y = 4


Line 1
y = -3x + 9
-2x + y = 4
Line 2
3x + (-3x + 9) = 9
Line 3
3x - 3x + 9 = 9
Line 4
9 = 9
Found 2 solutions by ValorousDawn, Boreal:
Answer by ValorousDawn(53) About Me  (Show Source):
You can put this solution on YOUR website!
Line 2. You don't plug in a variable's identity back into the original equation.
Otherwise, you get a useless statement, as above with 9=9 Given a linear equation ax%2Bby=c, and one isolates a term, for example, the y as such by=-ax%2Bc then y=-ax%2Fb%2Bc%2Fb. If you were to plug this back into the equation, you'd get ax%2Bb%28-ax%2Fb%2Bc%2Fb%29=c, then ax-ax%2Bc=c which is then c=c.
In this case, you'd plug in the equation for y y=-3x%2B9 into the OTHER equation. This gives you -2x%2B%28-3x%2B9%29=4 which gives you -5x=-5 or x=1. You then plug this into your equation for y, and solve. y=-3%281%29%2B9 y=6

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
-2x+y=4
-2x-3x+9=4
-5x=-5
x=1
The mistake is made in line 2. The first line is fine, but now the y =-3x+9 has to be substituted for y in the equation -2x+y=4, not back into the first equation where of course it will be 9=9.