Solve the system of equations using subtitution method if the answer is a unique solution, present it is order

Question

pair: x,y. If not, specifiy whether the answer is no solution or infinitely many soloution -3x +y =1
5x + 2y = -4

Answer 1

- 3x + y = 1- - - - - -Equation 1
5x + 2y = - 4- - - - -Equation 2
- - - - - - - - - -

Isolate the y variable in equation 1

- 3x + y = 1

- 3x + y + 3x = 3x + 1

y = 3x + 1

Substitute the y value into equation 2
- - - - - - - - - - - - - --

5x + 2y = - 4

5x + 2(3x + 1) = - 4

5x + 6x + 2 = - 4

11x + 2 = - 4

11x + 2 - 2 = - 4 - 2

11x = - 6

11x / 11 = - 6 / 11

x = - 6/11

Insert the x value into equation 1
- - - - - - - - -

- 3x + y = 1

- 3(- 6/11) + y = 1

-( - 18/11) + y = 1

18/11 + y = 1

18/11 + y - 18/11 = 1 - 18/11

y = 11/11 - 18/11

y = - 7/11

Insert the y value into equation 1
- - - - - - - - - -

Check for equation 1

- 3x + y = 1

- 3(- 6/11) + ( - 7/11) = 1

- (- 18/11) - 17/11 = 1

18/11 - 7/11 = 1

11/11 = 1

1 = 1

- - - - - - - - - -

Check for equation 2

5x + 2y = - 4

5(- 6/11) + 2( - 7/11) = - 4

- 30/11 + (- 14/11 + - 4

- 30/11 - 14/11 = - 4

- 44/11 = - 4

- 4 = - 4

- - - - - -- - -

Both equations balance

The solution set { - 6/11, - 7/11 }

- - - - - - - - - -s-

Answer 2

1) - 3x + y = 1
2) 5x + 2y = - 4

Solve equation 1 for y

y = 3x + 1

Substitute into equation 2

5x + 2(3x + 1) = - 4
5x + 6x + 2 = - 4
11x = - 6
x = - 6/11

Substitute into equation 1

- 3(-6/11) + y = 1
y = 1 - 18/11
y = - 7/11

Check in equation 2

5(-6/11) + 2(-7/11) = - 4
- 30/11 - 14/11 = - 4
- 44/11 = - 4
- 4 = - 4

Solution is (-6/11, -7/11)

Answer 3

solve for -3x + y = 1 for y
y = 3x + 1

Plug this into 5x + 2y = -4
5x + 2(3x + 1) = -4
5x + 6x + 2 = -4
11x = -6
x = -6/11

plug this into -3x + y = 1
-3(-6/11) + y = 1
18/11 + y = 1
y = 11/11 - 18/11
y = -7/11

so x = -6/11 and y = -7/11

Answer 4

y = 3x + 1
5x + 6x + 2 = - 4
11x = - 6
x = - 6 / 11

y = - 18 / 11 + 1
y = - 7 / 11

x = - 6 / 11 , y = - 7 / 11

Answer 5

based on first equation,
y = 1+3x
substitute into 2nd one
5x+2(1+3x)=-4
5x+2+6x=-4
11x=-6
x=-6/11
put this back in first one
y=1+3*-6/11
= (11-18)/11
y=-7/11

Answer 6

-3x+y=1
5x+2y=-4

y=1+3x

5x+2(1+3x)=-4
5x+2+6x=-4
11x=-6
x=-6/11
y=1+3x=1+3*-6/11=1-18/11=-7/11

x=-6/11
y=-7/11