Final answer:
To solve the given equations, isolate the unknown variables on one side by applying basic algebraic operations. Use the elimination or substitution method to solve for the variables.
Step-by-step explanation:
To solve the equations, we will apply basic algebraic operations to isolate the unknown variable on one side of the equation.
a) 3x+2y=10; solve for x, y, and z
There is no variable 'z' in the given equation. Therefore, there is no solution for 'z'.
To solve for 'x', we can isolate it by subtracting 2y from both sides:
3x = 10 - 2y
x = (10 - 2y)/3
To solve for 'y', we can isolate it by subtracting 3x from both sides:
2y = 10 - 3x
y = (10 - 3x)/2
b) 2a−4b=8; solve for a, b, c
There is no variable 'c' in the given equation. Therefore, there is no solution for 'c'.
To solve for 'a', we can isolate it by adding 4b to both sides:
2a = 8 + 4b
a = (8 + 4b)/2
To solve for 'b', we can isolate it by subtracting 2a from both sides:
-4b = 8 - 2a
b = (8 - 2a)/(-4)
c) 7p+5q=35; solve for p, q, r
There is no variable 'r' in the given equation. Therefore, there is no solution for 'r'.
To solve for 'p', we can isolate it by subtracting 5q from both sides:
7p = 35 - 5q
p = (35 - 5q)/7
To solve for 'q', we can isolate it by subtracting 7p from both sides:
5q = 35 - 7p
q = (35 - 7p)/5
d) 4m−2n=12; solve for m, n, p
There is no variable 'p' in the given equation. Therefore, there is no solution for 'p'.
To solve for 'm', we can isolate it by adding 2n to both sides:
4m = 12 + 2n
m = (12 + 2n)/4
To solve for 'n', we can isolate it by subtracting 4m from both sides:
-2n = 12 - 4m
n = (12 - 4m)/(-2)