The answer is in this explanation below.
To solve the given system of equations by substitution, we'll follow these steps:
1. Start with the first equation: x + y = 2z = -14.
2. Solve the first equation for x in terms of y and z:
x = -14 - y - 2z.
3. Substitute the expression for x into the second equation:
-3y + z = 7.
4. Simplify the equation:
-3y + z = 7.
5. Substitute the given value of z = 4 into the equation:
-3y + 4 = 7.
6. Solve for y:
-3y = 7 - 4,
-3y = 3,
y = -1.
7. Substitute the value of y = -1 back into the first equation to solve for x:
x + (-1) = 2(4) = -14,
x - 1 = 8,
x = 9.
8. Check the solution by substituting the values of x, y, and z into both equations:
For the first equation: 9 + (-1) = 2(4) = -14,
8 = 8, which is true.
For the second equation: -3(-1) + 4 = 7,
3 + 4 = 7, which is also true,
the solution to the system of equations is:
x = 9,
y = -1,
z = 4
Correct me if i'm wrong :>