How to solve the following system by the substitution method:?

Question

2x+5y=negative 4
3x-y=11

please explain step by step how to solve

Answer 1

[05]
2x+5y= -4.......(1)
3x-y=11
-y=11-3x
y=3x-11.....(2)
Substituting y by 3x-11 in (1)
2x+5(3x-11)= -4
2x+15x-55= -4
17x= -4+55=51
x=51/17=3
Plugging x in(2)
y=3*3-11= -2

Answer 2

Thanks for a very simple question. Follow my step below.

Firstly, given the equation:
2x + 5y = -4
3x - y = 11

Mark as (1) and (2):
2x + 5y = -4.....(1)
3x - y = 11.....(2)

From equation (2), we find y:
3x - y = 11
-y = 11 - 3x
y = 3x - 11.....(3)

Then, we substitute (3) into equation (1):
2x + 5y = -4
2x + 5(3x - 11) = -4
2x + 15x - 55 = -4
17x - 55 = -4
17x = -4 + 55
17x = 51
x = 51 ÷ 17
x = 3

Next, substitute x = 3 into equation (3):
y = 3x - 11
y = 3(3) - 11
y = 9 - 11
y = -2

Therefore, the answer should be:
x = 3 and y = -2

I hope you got the best answer for your question. Have a nice day!

Answer 3

The point of the substitution method is to take a complicated system and substitue something not so complicated into the system.
Given the two systems, you assume that the same values for x and y will work in both systems.
The second statement is the simplest form. With a coefficient of -1y, manipulate the statement to get a positive y alone on one side:
add -11 and y to both sides. Simplify to get 3X - 11 = y
Substitue (3x -11) for y in the first statement so that you have:
2x +5(3x-11) = (-4)
Multiply through and Solve for X, then find Y by substituting the known value for X.

Answer 4

Isolate one of the variables in either equation. In this case, the easiest to isolate will be the y in the second equation.

Add y to both sides and subtract 11 from both sides to get:
3x - 11 = y

In the first equation, everywhere you see a y, substitute in a 3x-11. You get:

2x + 5(3x-11)= -4
2x + 15x - 55 = -4
17x = 51
x = 3

In the second equation, everywhere you see an x, substitute a 3 to get:

3*3 - y = 11
9 - 11 = y
-2 = y

Answer 5

Okay, to make this easier, set y=3x-11:

3x-y=11
3x=y+11
3x-11=y

Then substitute 3x-11 in for 2x+5y=-4:

2x+5(3x-11)=-4

Distribute:

2x+15x-55=-4

Simplify:

17x-55=-4

Add 55 over to the other side:

17x=55-4
17x=51

Divide:

17x=51
x=3

Substitute 3 into the original problem:

3(3)-y=11
9-y=11

Subtract 9 onto the opposite side:

-y=11(-9)
-y=2

Divide by -1 on both sides to make y positive:

y=-2

Answer 6

Rearrange the second equation to 3x-11=y.

THen subsitute the left side of the equation into 2x+5(3x-11)= -4.

Answer 7

y = 3x - 11
2x + 15x - 55 = - 4
17x = 51
x = 3

9 - y = 11
y = - 2

x = 3 , y = - 2