please help me in subtitution method?

Question

please help me to answer this 2 problem ?
this is subtitution method

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

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

please send me the answer in my email [e-mail] i have classes later..
please help me.. because i am not good in mathematics...

thank you so much

Answer 1

I will email this answer to you, but for others, here is the answer:

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

The second equation gives you the value of x.
So substitute that expression into the first equation for x:
2(y - 5) + y = -4

Now, solve for y.
2y - 10 + y = -4
3y = 6
y = 2

Now that you know the value of y, substitue that value in the second equation (you could do the first, but the second is easier) and solve for x:
x = 2 - 5
x = -3

So, x = -3 and y = 2.

Plug these numbers back into the original equations to check your answer:
2(-3) + 2 = -4
-6 + 2 = -4 (true)

-3 = 2 - 5 (true)
___________________

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

Solve this the same way, substituting the known expression for y from the first equation into the second:

2x - 4(2x + 1) = 3
2x - 8x - 4 = 3
-6x = 7
x = - 7/6

Now solve for y by substituting x into the first equation:
y = 2(-7/6) + 1
y = -14/6 + 1
y = -7/3 + 3/3
y = -4/3

So, x = -7/6 and y = -4/3.

Plug these numbers back into the original equations to check your answer:
-4/3 = 2(-7/6) + 1
-4/3 = -14/6 + 1
- 8/6 = -14/6 + 6/6 (true)

2(-7/6) - 4(-4/3) = 3
-14/6 + 16/3 = 3
-14/6 + 32/6 = 18/6 (true)

Answer 2

1. Since x = y - 5, then
...y = x + 5
...substitute x + 5 for y into the first equation:
...2x + x + 5 = -4
...3x + 5 = -4
...3x = -9
...x = -3
...y = 2

2. Since y = 2x + 1
...substitute 2x + 1 for y into the second equation:
...2x - 4(2x + 1) = 3
...2x - 8x - 4 = 3
...-6x = 7
...x = -7/6
...y = -4/3

Answer 3

1. Since x = y - 5, then
...y = x + 5
...substitute x + 5 for y into the first equation:
...2x + x + 5 = -4
...3x + 5 = -4
...3x = -9
...x = -3

2. Since y = 2x + 1
...substitute 2x + 1 for y into the second equation:
...2x - 4(2x + 1) = 3
...2x - 8x - 4 = 3
...-6x = 7
...x = -7/6

Answer 4

1) 2x + x + 5 = -4
3x = -9
x = -3

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

2) 2x - 4(2x+1) = 3
-6x = 7
x = -7/6

y = 2x-7/6 + 1 = -4/3

Answer 5

2x + y = -4

x = y -5

2(y -5)+y=-4
2y-10+y=-4
3y=6
y=2

x=-3

---------------------

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

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

2x-8x-4=3
-6x-4=3
-6x=7
x=-7/6

y = 2x + 1

2(-7/6)+1=-14/6+6/6=-8/6
y=-4/3