solve simultaneously
0.5m +0.2n # 5........(1)
0.6m +0.4n # 8.4.......(2)?
what, your keyboard has no = key?
multiply the first equation by 2 and you now have
1.0m + 0.4n = 10
0.6m + 0.4n = 8.4
now subtract the 2nd from the 1st, and the n's go away, leaving
0.4m = 1.6
Now you can finish up. Find m, then use that in either equation to find n.
To solve the system of equations simultaneously, we'll use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve equation (1) for m:
0.5m + 0.2n = 5
0.5m = 5 - 0.2n
m = (5 - 0.2n) / 0.5 (equation (3))
Step 2: Substitute the value of m from equation (3) into equation (2) and solve for n:
0.6m + 0.4n = 8.4
0.6[(5 - 0.2n) / 0.5] + 0.4n = 8.4
Now we can solve this equation for n.
Step 3: Simplify the equation by multiplying both sides by the common denominator 0.5:
0.6(5 - 0.2n) + 0.4n = 8.4
3 - 0.12n + 0.4n = 8.4
Step 4: Combine like terms:
-0.12n + 0.4n = 8.4 - 3
0.28n = 5.4
Step 5: Solve for n by dividing both sides by 0.28:
n = 5.4 / 0.28
n ≈ 19.2857
Step 6: Substitute the value of n back into equation (3) to solve for m:
m = (5 - 0.2(19.2857)) / 0.5
m ≈ 0.4286
Therefore, the solution to the system of equations is m ≈ 0.4286 and n ≈ 19.2857.