x-z=7
x+y=3
z-y=6
For the above system of three equations
x= ?
To find the value of x in the given system of equations, we can use the method of elimination or substitution. Let's use the method of substitution to solve this system.
1) Start with the first equation: x - z = 7.
2) Solve this equation for x:
x = z + 7.
3) Now substitute this value of x into the second equation: x + y = 3.
(z + 7) + y = 3.
4) Rearrange this equation by combining like terms:
z + y + 7 = 3.
5) Rewrite this equation as:
z + y = -4.
6) Now we have two simplified equations:
z + y = -4 (Equation 1)
z - y = 6 (Equation 2).
7) Add Equation 1 and Equation 2:
(z + y) + (z - y) = -4 + 6.
z + y + z - y = 2.
2z = 2.
8) Divide both sides of the equation by 2 to solve for z:
z = 1.
9) Substitute this value of z into Equation 1:
1 + y = -4.
10) Solve this equation for y:
y = -5.
11) Now substitute the values of z and y into the equation x = z + 7:
x = 1 + 7.
12) Solve this equation for x:
x = 8.
Therefore, the solution to the given system of equations is x = 8.