Answer
$(t,h)= (1.80,-4.30)$
Work Step by Step
Given: $$\begin{cases}
1.4h-2.6t &= -10.7\\
3h & =6.9t-25.32.
\end{cases}$$ We are asked to use the method of substitution to solve the given system. First, rewrite the second equation in the slope intercept form and substitute the result into the first equation. $$\begin{aligned}
3h & =6.9t-25.32 \\
h &=\frac{6.9t-25.32}{3} \\
h &= 2.3t-8.44.
\end{aligned}$$ Do the substitution:
$$\begin{aligned}
1.4(2.3t-8.44)-2.6t &= -10.7\\
3.22t-2.6t-11.816 &=-10.7 \\
0.62t&= 11.816-10.7\\
t&= \frac{1.116}{0.62}\\
&= 1.80.
\end{aligned}$$ Now find $h$ using any one of the equations given. $$\begin{aligned}
h &= 2.3\cdot(1.80)-8.44\\
&= -4.30.
\end{aligned}$$ Check the solution: $$\begin{aligned}
1.4\cdot(-4.3)-2.6\cdot(1.8) &= -10.7\\
-10.7& =-10.7.
\end{aligned}$$ $$\begin{aligned}
3\cdot(-4.3) &= 6.9\cdot 1.8-25.32\\
-12.9& =-12.9.
\end{aligned}$$ The solution set is $(t,h)= (1.80,-4.30)$. The system is consistent and independent because it has a single solution.
