Show and explain EACH step in solving the following system of equations by the substitution method.?

Question

Show and explain EACH step in solving the following system of equations by the substitution method.
a: 0.4x - 0.1y = 5 and 6.4x + 0.4y = 60

Answer 1

GIVEN:

0.4x - 0.1y = 5
6.4x + 0.4y = 60

STEP 1: Multiply the first equation by 4 to get the following: (because notice that 0.1 * 4 = 0.4, and we will be able to cancel our y's out and solve for x)

1.6x - 0.4y = 20
6.4x + 0.4y = 60

STEP 2: Add the two equations together, to get one equation with our x variable only:

1.6x - 0.4y = 20
6.4x + 0.4y = 60
-----------------------
8.0x + 0y = 80

STEP 3: Divide both sides by 8 to solve for x:

x = 10

STEP 4: Substitute this value for x into either one of your original 2 equations to solve for y:

0.4x - 0.1y = 5
0.4(10) - 0.1y = 5
4 - 0.1y = 5
-0.1y = 1
0.1y = -1
y = -10

FINAL STEP: Your answers are x = 10, y = -10

Hope that helped!

~ ♥ ~

Answer 2

Get rid of decimals first by multiplying each
equation by 10. It makes it so much easier.

Equation 1 : 4x - y = 50
Equation 2 : 64x + 4y = 600

Now equation 2 can be divided through by 4
to give : 16x + y = 150

Now we have :

Equation 1 : 4x - y = 50
Equation 2 : 16x + y = 150

Add them together to get : 20x = 200, so x = 10.

Substitute this back into equation 1, for example.
4(10) - y = 50, so y = -10.

Answer 3

0.4x - 0.1y = 5 multiply by 10
4x-y=5 subtract 5 from each side
4x-5-y=0
add y to each side
y=4x-5
substitut en eqn below.
6.4x + 0.4y = 60
6.4x+.4(4x-5)=60 distribute .4
6.4x+1.6x-2=60
8x-2=60 add 2
8x=62
divide by 8
x=62/4=31/4
substitute to find y
y=4x-5
y=4(31/4)-5=31-5=26

solution is (31/4,26)

Answer 4

0.4x - 0.1y = 5
0.4x = 5 + 0.1y (moving y over to one side)
x = 5/0.4 + (0.1/0.4)*y (divide by 0.4)
x=12.5+0.25y

substitute x into second equation:
6.4(12.5+0.25y) + 0.4y = 60
80+1.6y+0.4y=60 (simplify the equation)
80+2y=60
20+2y=0 (subtract both sides by 60)
2y=-20 (simplify)
y=-10
x=12.5+0.25(-10)=12.5-2.5=10 (solve for x)

Answer 5

The primary method I use is....going to school and doing my homework and NOT relying on yahoo answers to do it for me.