If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the third equation.
2x - 3y + z = -4
2x - 2y + z = -1
x - 2y + 3z = -6
5x + 7y = 6
y - 4 = -1
-y - 1 = -4
-5x + 4y = -3
y - 5z = 8
2y - 5z = 11
-7y + 7z = 8
-6y + 7z = 11
The answer is:
-y - 1 = -4
-5x + 4y = -3
To isolate x in the third equation using the substitution method, we can start by rewriting the equation:
x - 2y + 3z = -6
To isolate x, we can add 2y and subtract 3z from both sides of the equation:
x = 2y - 3z - 6
Now, using x = 2y - 3z - 6, we can substitute this expression of x into the first two equations of the original system:
2x - 3y + z = -4
2x - 2y + z = -1
Substituting x = 2y - 3z - 6, we get:
2(2y - 3z - 6) - 3y + z = -4
2(2y - 3z - 6) - 2y + z = -1
Simplifying each equation:
4y - 6z - 12 - 3y + z = -4
4y - 6z - 12 - 2y + z = -1
Combining like terms:
y - 5z = 8
2y - 5z = 11
Therefore, the new system of equations after isolating x in the third equation is:
y - 5z = 8
2y - 5z = 11