Question

Solve the given system of equations utilizing either the substitution or addition method.

Answer 1

Value of x=4 and y=-13/3

Explanation:

We need to solve the systems of equations

`5x+3y=7 \ and \ (3)/(2)x-(3)/(4)y =9(1)/(4)`

Solving using substitution method:

Let:

`5x+3y=7---eq(1) \\ (3)/(2)x-(3)/(4)y =9(1)/(4)---eq(2)`

Find value of x from eq(1) and put in eq(2)

`5x+3y=7\\5x=7-3y\\x=(7-3y)/(5)`

Put value of x in eq(2)

`(3)/(2)((7-3y)/(5)) -(3)/(4)y =(37)/(4)\\(21-9y)/(10) -(3)/(4)y =(37)/(4)\\Taking \ LCM\\(21*2-9y*2-3y*5)/(20) =(37)/(4)\\(42-18y-15y)/(20) =(37)/(4)\\42-33y=(37)/(4)*20\\42-33y=185\\-33y=185-42\\-33y=143\\y=(143)/(-33)\\y=-(13)/(3)`

Now, finding value of x by putting value of y in eq(1)

`x=(7-3y)/(5)\\x= (7-3(-(13)/(3)) )/(5)\\x=(7+13)/(5)\\x=(20)/(5)\\x=4`

So, Value of x=4 and y=-13/3