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!
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.
Solve the following system of equations by the substitution method.
8x = 2y + 5
3x = y + 7
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
x=4,y=0
To solve this system of equations using the substitution method, you need to solve one equation for one variable, and then substitute that expression into the other equation. Let's start with the first equation, y - x = 4.
Step 1: Solve the first equation for one variable.
Adding x to both sides, we get:
y = x + 4
Step 2: Substitute the expression into the second equation.
Now, substitute y = x + 4 into the second equation, x - y = 3:
x - (x + 4) = 3
Step 3: Simplify and solve for x.
Distribute the negative sign:
x - x - 4 = 3
-4 = 3
This is where the problem arises. -4 cannot be equal to 3. Therefore, there is no solution to this system of equations.
So, your original answer of x and y = 7/2 is incorrect. The book is correct in stating that there is no solution. Your mistake most likely occurred during the substitution step or simplifying the equation. Make sure to double-check your calculations to identify where the error may have occurred.