a equivalent system question?

Question

3m+4t=10
1.2m+10t=9.8

could someone show me the work it would take to find the values for m and t?
thanks.

Answer 1

There are a few different ways... Using a matrix is one, but that's hard to do on this forum... I'll use substitution method...

Solve one equation for one variable:

1.2m + 10t = 9.8
10t = 9.8 - 1.2m
t = 0.98 - 0.12m

Now, take t and plug it into the other equation and solve for m.
3m + 4t = 10
3m + 4(0.98 - 0.12m) = 10
3m + 3.92 - 0.48m = 10
2.52m + 3.92 = 10
2.52m = 6.08
m = 2.41 (rounded)

Now take that m and put it back into the first equation:
t = 0.98 - 0.12m
t = 0.98 - 0.12(2.41)
t = 0.98 - 0.2892
t = 0.69 (rounded)

Answer 2

3m + 4t = 10- - - - - - Equation 1
1.2m + 10t = 9.8-- - -- Equation 2
- - - - - - - - - - - - -

Multiply equation 1 by 5 and equation 2 by - 2

5(3m) + 5(4t) = 5(10)

15m + 20t = 50. . .New equation 1
- - - - - - -

-2(1.2m) + ( - 2)(10t) = - 2(9.8)

- 2.4 - 20t = - 19.6 . ..New equation 2

- - - - - - - -

15m + 20t = 50
- 2.4m - 20t = - 19.6
- - - - - - - - - - - - -

12.6m = 30.4

12.6m/12.6 = 30.4/12.6

m = 2.412698413

The answer is m = 2.412698413

Insert the m value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

1.2m + 10t = 9.8

1.2(2.412698413 + 10t = 9.8

2.895238095 + 10t = 9.8

2.895238095 + 10t - 2.895238095 = 9.8-2.895238095

10t = 6.904761905

10t/10 = 6.904761905 / 10

t =0.69047619

The answer is t = 0.69047619

- -- - - - -- s-

Answer 3

3m+4t=10
m= (10-4t)/3
Subtitute in equation 1.2m+ 10t= 9.8
1.2 ( (10-4t)/3)+ 10t= 9.8
(12-4.8t)/3+ 10t=9.8
12-4.8t +30t =29.4
25.2t= 17.4
t= 0.69

Replace value of t in m=(10-4t)/3
m= (10-4*0.69)/3
m=2.41

Answer 4

multiply eq 1 by 0.4 on both sides, we get

1.2m + 1.6 t = 4 eq (1')
1.2m + 10 t =9.8 eq 2, now subtract eq1' from eq2, we get

8.4 t = 5.8 or

t = 29/42 = 0.69 > put in eq1

3m = 10 - 4*29/42 = 152/21 >

m = 152/63 = 2.41

Answer 5

Multiplying the second equation by ten, on both sides, we get,
12m + 100t = 98..............(3)
Multiplying the first equation by 4, on both sides we get,
12m + 16t = 40.................(4)
Eqn (3) minus eqn (4) gives,
84t = 58
Or t = 58/84 = 0.7

Substituting the value of t in eqn (3), one obtains
12m + 70 = 98
Or 12m = 28
Or m = 28/12 = 7/3 = 2.3

Answer t = 0.7 and m = 2.3, approximately i.e., up to one place of decimal.