# Linear Equations

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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 -

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 -

Solve the following system of equations by the substitution method.

8x = 2y + 5
3x = y + 7

• Linear Equations -

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

• Linear Equations -

x=4,y=0