Answer: The required solution is (x, y) = (1.4, 2.1).
Step-by-step explanation: We are given to solve the following system of equations by the method of substitution :
[tex]7+2y=8x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-2y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]3x-2y=\\\\\Rightarrow 3x=2y\\\\\Rightarrow x=\dfrac{2}{3}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (i), we get
[tex]7+2y=8\times\dfrac{2}{3}y\\\\\Rightarrow 21+6y=16y\\\\\Rightarrow 16y-6y=21\\\\\Rightarrow 10y=21\\\\\Rightarrow y=\dfrac{21}{10}.\\\\\Rightarrow y=2.1[/tex]
From equation (iii), we get
[tex]x=\dfrac{2}{3}\times\dfrac{21}{10}=\dfrac{7}{5}=1.4.[/tex]
Thus, the required solution is (x, y) = (1.4, 2.1).
