Posted by **Mia** on Tuesday, March 2, 2010 at 1:04pm.

Can you please help solve this equation using the substitution method? I have tried and keep getting that X and Y = 7/2, but the answer in the book states no solution, inconsistent system. What am I doing wrong? Please help! Solve the systems of equations by the substitution method.

y-x=4

x-y=3

Thank you!

- Linear Equations -
**Reiny**, Tuesday, March 2, 2010 at 4:14pm
Here is why there is no solution ...

multiply the first equation by -1

x - y = -4

subtract the second equation ...

0 = -7 >>>> CONTRADICTION! So, no solution.

OR

by substitution,

first equation: y = x+4

sub into second

x-y = 3

x - (x+4) = 3

x-x-4=3

0 = 7, same result.

Your answer of x = y = 7/2 does not work in either equation.

- Linear Equations -
**megan**, Thursday, June 30, 2011 at 10:22am
Solve the following system of equations by the substitution method.

8x = 2y + 5

3x = y + 7

- Linear Equations -
**jessica**, Saturday, February 16, 2013 at 6:06am
Y-X=4...(EQN 1)

X-Y=3...(EQN 2)

MAKING X THE SUBJECT IN EQN 2

X=3+Y

SUBSTITUTING IN EQN 1

Y-(3+Y)=4

Y-3-Y=4

THE Y GETS ELIMINATED,HENCE THERE IS NO SOLUTION

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