Algebra - Substitution Question?
A+B+C=1
A+C= -1/2
A-B+C= -7
What are the values of A, B, and C?
Subtract the third equation from the second and you get
B = 6 1/2
Subtract the second from the first and you get B = 3/2
Both cannot be true, so there is no solution.
that's what i got too
To solve this system of equations using substitution, we'll start by solving one equation for a specific variable, and then substitute that expression into the other equations. Let's solve the second equation for A:
A + C = -1/2
By isolating A, we can subtract C from both sides:
A = -1/2 - C
Now, substitute this expression for A in the first and third equations:
1) A + B + C = 1
(-1/2 - C) + B + C = 1
2) A - B + C = -7
(-1/2 - C) - B + C = -7
Now, simplify both equations:
1) -1/2 - C + B + C = 1
B - 1/2 = 1
2) -1/2 - C - B + C = -7
-B - 1/2 = -7
To solve these equations, isolate B in equation 1:
B = 1 + 1/2
B = 3/2
Now, substitute this value of B into equation 2:
-(3/2) - 1/2 = -7
-4/2 = -7
-2 = -7
This is not a true statement, which means there is no solution. The system of equations is inconsistent, and there are no values for A, B, and C that satisfy all three equations simultaneously.
Hence, there are no values for A, B, and C.