Question

Question 3(Multiple Choice Worth 4 points)

(08.03)Solve the system of equations and choose the correct answer from the list of options.

2x + y = −4
y = 3x + 2

negative 6 over five comma negative 8 over 5
negative 8 over 5 comma negative 6 over 5
negative 5 over 6 comma negative 11 over 5
negative 11 over 5 comma negative 6 over 5

Answer 1

The solution of the system of equations is:

negative 6 over 5 comma negative 8 over 5.

Explanation:

We are given a system of linear equations as:

2x + y = −4 ------------(1)

y = 3x + 2------------(2)

Now we solve the system of equations using the substitution method.

i.e. we substitute the value of y in terms of x from equation (2) in equation (1) and find the value of x and y.

i.e.

2x+3x+2= -4

i.e. 5x+2= -4

i.e. 5x= -6

i.e. x= -6/5

Similarly, on putting this value of x in equation (2) we obtain:

y= -8/5

Hence, the solution is:

`(-(6)/(5),-(8)/(5))`

Answer 2

subsitution

y=3x+2
subsitute (3x+2) for y in other equation

2x+y=-4
2x+(3x+2)=-4
2x+3x+2=-4
5x+2=-4
minus 2 both sides
5x=-6
divide both sides by 5

`x=(-6)/(5)`

subsitute back


`y=3x+2`

`y=3((-6)/(5))+2`

`y=(-18)/(5)+2`

`y=(-18)/(5)+(10)/(5)`

`y=(-18+10)/(5)`

`y=(-8)/(5)`



`x=(-6)/(5)`

`y=(-8)/(5)`

(x,y)

`((-6)/(5),(-8)/(5))`



the solution is
`((-6)/(5),(-8)/(5))`
that is the first option