Question

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 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 :

`5x-3y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\7x+4y=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

We will be using the method of SUBSTITUTION to solve the given system.

From equation (i), we have

`5x-3y=11\\\\\Rightarrow 5x=11+3y\\\\\Rightarrow x=(11+3y)/(5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x from equation (iii) in equation (ii), we get

`7x+4y=-1\\\\\\\Rightarrow 7*(11+3y)/(5)+4y=-1\\\\\\\Rightarrow 77+21y+20y=-5\\\\\Rightarrow 41y=-5-77\\\\\Rightarrow 41y=-82\\\\\Rightarrow y=-(82)/(41)\\\\\Rightarrow y=-2.`

Putting the value of y in equation (iii), we get

`x=(11+3*(-2))/(5)=(11-6)/(5)=(5)/(5)=1.`

Thus, the required solution is x = 1 and y = -2.