Question

Using three variables, create (make up) an equation. After you have made your equation, solve it 3 different times. You will end with three answers all solved for different variables. For example, 5c/f=1/r, solve for r, c and f. Show all of your steps.

a) 3x+2y=10; solve for x, y, and z
b) 2a−4b=8; solve for a, b, c
c) 7p+5q=35; solve for p,q,r
d) 4m−2n=12; solve for m,n,p

Answer 1

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)