SOLUTION: Solve by the substitution method x + y = 2 x + y = -9

Question 170659This question is from textbook Introductory Algebra
: Solve by the substitution method
x + y = 2
x + y = -9 This question is from textbook Introductory Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Combine like terms on the left side

Subtract 2 from both sides

Combine like terms on the right side

Simplify

Since this equation is NEVER true for any x value, this means there are no solutions.

So the system is inconsistent.

RELATED QUESTIONS
Solve by the substitution method. x + y = 2 x + y =... (answered by jim_thompson5910,checkley77)

solve by substitution method x+y=-9... (answered by stanbon)

Solve the system by the substitution method. -2x + y = -2 x - 4y = 9 (answered by jim_thompson5910)

Solve each system by substitution method 1) y=x^2+6x+9 2) x+y=3 (answered by tommyt3rd)

solve the system x+y=6 and x=y+2 by the substitution method (answered by Fombitz)

Solve the system by the substitution method. 2x+y-x=3y+5... (answered by waynest)

solve the system by the method of substitution x=y+3 x=y^2+1 (answered by MathLover1)

Solve by substitution method 3x+y=2... (answered by jim_thompson5910)

solve by substitution method y=2x-5... (answered by Boreal)