math help! systems of linear equations?

Question

i have to solve this by using substitution please show work and explain each step and why u did it (add subtract multiply etc.)
4x-y=-4
-2x+5y=29

im getting so confused on this and a good example and explanation of step by step process would be greatly appreciated

Answer 1

y = 4x + 4

- 2x + 5(4x + 4) = 29
- 2x + 20x + 20 = 29
18 x = 9
x = 1 / 2

y = 6

Answer 2

If you are going to use substitution, look for a coefficient of 1 or -1 on the variables. That is the easiest one to work with.

In your example, the top equation 4x - y = -4, there is a coefficient of -1 on y. So solve that equation for y.

Move the y to the left and the 4 to the right, which changes both of their signs.

4x + 4 = y

Now, 4x + 4 and y are equivalent, so replace the y in the second equation with 4x + 4

-2x + 5(4x + 4) = 29

Simplify the equation
-2x + 20x + 20 = 29
-18x + 20 = 29

Solve for x
-18x = 29 - 20
-18x = 9
x = -9/18 = -1/2

Now, that you know the value of x, go back to y = 4x + 4 and replace x with -1/2

y = 4(-1/2) + 4
y = -2 + 4
y = 2

Now that you know x and y, write the answer as an ordered pair (x, y)

(-1/2, 2)

Answer 3

Values of y:
4x - y = - 4
y = 4x + 4

- 2x + 5y = 29
5y = 2x + 29
y = (2x + 29)/5

Value of x:
4x + 4 = (2x + 29)/5
20x + 20 = 2x + 29
18x = 9
x = 1/2

Value of y:
= 4(1/2) + 4
= 2 + 4
= 6

Answer: x = 1/2, y = 6

Proof 1:
4(1/2) - 6 = - 4
2 - 6 = - 4

Proof 2:
- 2(1/2) + 5(6) = 29
- 1 + 30 = 29

Answer 4

4x - y = - 4 (eq.1)
-2x + 5y = 29 (eq.2)

solving by sustitution:

first find the in equation that is easy to get the first uknown variable with the coefficient o 1.

we use eq.1,

4x - y = - 4,

using transposition, the sign will changed.

4x + 4 = y

now we have value of y in terms of x, substitute to the eq.2

-2x + 5 ( 4x + 4 ) = 29

simplify,

- 2x + 20x +20 = 29

combining like terms,

-2x + 20x = 29 - 20

simplify it,

18x = 9
18x / 18 = 9 / 18

solving for x,

x = 1/ 2

now we have the x value, we can substitute this value to our eq.1 or eq. 2

we used eq.1

4x - y = - 4

4(1 / 2) - y = - 4

2 - y = -4

2 + 4 = y

y = 6

hope you get it,

Answer 5

4x-y=-4
-2x+5y=29

taking the first equation rearrange for y.

4x=y-4
4x+4=y

Now this can be substituted into the second equation.

So -2x+5(4x+4)=29

Now solve this for x.

-2x+20x+20=29
18x=9
x=1/2

Now we can use this value of x in the first equation to find y.

4(1/2)-y=-4
2-y=-4
-y=-6
y=6

So the answer is x=1/2 and y=6

Answer 6

2 the right thank you to unravel: #a million: removal x+2y=0 2x-6y=5 Multiply equation a million with the aid of 3 3x+6y=0 2x-6y=5 -----------upload 5x=5 x=a million replace a million for x into the two of the two unique equations. x+2y=0 a million+2y=0 2y=-a million y= -a million/2 #2: Substitution x+2y=0 2x-6y=5 From Equation No.a million, x=-2y replace x with -2y in Equation No.2 2(-2y)-6y=5 -4y-6y=5 -10y=5 y= -a million/2 As in the previous, replace y with -a million/2 in the two unique equation. 2x-6y=5 2x-6(-a million/2)=5 2x+3=5 2x=2 x=a million Take your %.!