Math

QuestionSolve the equations: 2s13t=102s - \frac{1}{3}t = 10 and 5s=t+12s5s = t + 12 - s. Choose the correct statement about solutions.

Studdy Solution

STEP 1

Assumptions1. We are given a system of two linear equations in two variables, ss and tt. . The system of equations is $ \begin{array}{l} s-\frac{1}{3}t=10 \\ 5s=t+12-s \end{array} \]
3. We are asked to find the solution to this system of equations.

STEP 2

First, let's rewrite the second equation in the form ax+by=cax + by = c to make it easier to manipulate. We can do this by moving the ss term on the right side to the left side and the tt term on the right side to the left side.
5s+s=t+125s + s = t +12

STEP 3

implify the left side of the equation to get6s=t+126s = t +12

STEP 4

Now, let's isolate tt in the above equation by moving the 1212 to the left side6s12=t6s -12 = t

STEP 5

Now we have two equations in the form ax+by=cax + by = c2s13t=10s12=t\begin{array}{l} 2s-\frac{1}{3}t=10 \\ s -12 = t\end{array}

STEP 6

We can now substitute the expression for tt from the second equation into the first equation. This will give us an equation in terms of ss only.
2s13(6s12)=102s-\frac{1}{3}(6s -12)=10

STEP 7

implify the equation by distributing the 13-\frac{1}{3} across the terms in the parentheses2s2s+4=102s -2s +4 =10

STEP 8

implify the left side of the equation to get4=104 =10

STEP 9

This is a contradiction, since 44 is not equal to $$. This means that the system of equations has no solution.
So, the correct answer is (a) There is no solution to the system of equations.

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