Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work. 5x - 3y = 11 7x + 4y = -1

Answer:  The required solution is  x = 1  and  y = -2.Step-by-step explanation:  We are given to solve the following system of equations using substitution, elimination by addition or augmented matrix methods :[tex]5x-3y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\7x+4y=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]We will be using the method of SUBSTITUTION to solve the given system.From equation (i), we have[tex]5x-3y=11\\\\\Rightarrow 5x=11+3y\\\\\Rightarrow x=\dfrac{11+3y}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]Substituting the value of x from equation (iii) in equation (ii), we get[tex]7x+4y=-1\\\\\\\Rightarrow 7\times\dfrac{11+3y}{5}+4y=-1\\\\\\\Rightarrow 77+21y+20y=-5\\\\\Rightarrow 41y=-5-77\\\\\Rightarrow 41y=-82\\\\\Rightarrow y=-\dfrac{82}{41}\\\\\Rightarrow y=-2.[/tex]Putting the value of y in equation (iii), we get[tex]x=\dfrac{11+3\times(-2)}{5}=\dfrac{11-6}{5}=\dfrac{5}{5}=1.[/tex]Thus, the required solution is  x = 1  and  y = -2.