what is the value of y in the system of equation of equations below 3x+y+2z=-10 x+5y-2z=-12 -2x+3y=-1
To solve the system of equations, we will use the method of substitution.
First, we will solve the third equation for x in terms of y:
-2x + 3y = -1
-2x = -3y - 1
x = (3y + 1) / -2
Next, we will substitute this value of x into the first equation:
3x + y + 2z = -10
3((3y + 1) / -2) + y + 2z = -10
(9y + 3) / -2 + y + 2z = -10
9y + 3 - 2y + 4z = -20
7y + 4z = -23 ------------------(4)
Lastly, we will substitute this value of x into the second equation:
x + 5y - 2z = -12
((3y + 1) / -2) + 5y - 2z = -12
3y + 1 - 10y - 4z = -24
-7y - 4z = -25
Now we have a system of two equations with two variables:
-7y - 4z = -25 ------------------(5)
7y + 4z = -23 ------------------(6)
Adding equation (5) and equation (6) together, we get:
0 = -48
Since 0 does not equal -48, there is no solution that satisfies all three equations simultaneously. Therefore, there is no value of y in this system of equations.