Solve the system : 2t+3u = 14   t-5u = -3

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We have to find t and u using the equations

2t + 3u = 14 ...(1)

t - 5u = -3 ...(2)

(1) - 2*(2)

=> 2t + 3u - 2t + 10u = 14 + 6

=> 13u = 20

=> u = 20/13

substituting u= 20/13 in (2)

=> t = -3 + 100/13

=> t = 61/13

Therefore t = 20/13 and u = 61/13

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Given the system:

2t + 3u = 14.............(1)

t- 5u = -3.................(2)

We will use the substitution method to solve.

Let us rewrite (2).

==> t= 5u -3

Now we will substitute with t into (1)

==> 2t + 3u = 14

==> 2 (5u-3) + 3u = 14

==> 10u - 6 + 3u = 14

==> 13u = 14+6

==> 13u = 20

==> u = 20/13

==> t= 5u-3 = 5(20/13) - 3 = (100/13 - 39/13 = 61/13

==> t= 61/3

Then, the solution to the system is:

u = 20/13.

t= 61/13

Approved by eNotes Editorial Team

Posted on

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