Substatution method please help?

Question

Well ive been working on the subs method for a long time now and I kind of don't get partly due to my spacing out at times and my fat cow tracher who doesnt help me at all anywho I would like to know if it is nto too much to ask on how to solve these problems step by step, thanks:
y=4x
y=-x-15
________
b=a+5
b=3a-1
_______
y=1/2x
Y=5/2x+8
________
Oh btw this is my homework but I don't get it At all so that is why I turn to here :D

Answer 1

Question 1
4x = - x - 15
4x + x = - 15
5x = - 15
x = - 3
y = - 12

Question 2
3a - 1 = a + 5
3a - a = 5 + 1
2a = 6
a = 3
b = 8

Question 3
(1/2) x = (5/2)x + 8
x = 5x + 16
0 = 4x + 16
4x = - 16
x = - 4
y = (1/2)x
y = (1/2)(-4)
y = - 2

x= - 4 , y = - 2

PS
It is all too easy to blame the teacher!!

Answer 2

For the first one you have what both of the y's equal you need to get an equation where the x and y value are on the same side of the equal side

y = 4x
x + y = -15

Now substitute the y value into the second equation

x + 4x = -15
5x = -15

Divide through by 5 to get the variable alone

x = -3

Now plut -3 back in for x

y = 4(-3)
y = -12

Check:

-12= 4(-3) -12= -(-3) - 15
-12 = -12 -12 = 3 -15
-12 = -12

Same for the second one

b = a+ 5
-3a +b = -1

-3a + a+ 5 = -1
-2a = -6
a = 3

b = 3 + 5
b = 8

Check:
8 = 3 + 5 8 = 3(3) - 1
8 = 8 8 = 9 - 1
8 = 8

For the next one I would change the fractions to decimals (easier to work with)

y = .5x
-2.5x + y = 8

-2.5x + .5x = 8
-2.0x = 8
x = -4

y = .5(-4)
y = -2

-2 = .5(-4) -2 = 2.5(-4) + 8
-2 = -2 -2 = -10 + 8
-2 = -2


I sure hope this helps

Answer 3

y = 4x
y = -x - 15
4x = -x - 15
5x = -15
x = - 3
y = - 12

b= a + 5
b= 3a - 1
3a + 5 = 3a - 1
0 = 4
No solution

y = 1/2x
y = 5/2x + 8
1/2x = 5/2x + 8
-2x = 8
x = -4
y = -2

Answer 4

set each equal to each other
isolate the variable
solve for the variable
plug the answer into the original equation

4x = -x -15
5x = -15
x = -3
y = 4(-3)
y = -12
x=-3, y=-12
__________

a+5 = 3a -1
6 = 2a
a=3
b = (3) + 5
b=8
a= 3, b=8
__________

1/2x = 5/2x+8
2x = -8
x = -4
y = 1/2 (-4)
y = -2
x=-4, y=-2

Answer 5

1)
put y = 4x in 2nd eq

4x = -x -15
5x = -15
x = -3

y = 4(-3)
y = -12

2)
put b = a + 5 in 2nd eq

a + 5 = 3a - 1
6 = 2a
a = 3

b = 3 + 5
b = 8

3)
put y = 1/2x in 2nd eq
1/2x = 5/2x + 8
x = 5x + 16
4x = -16
x = -4

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

Answer 6

y=4x
y=-x-15

4x=-x-15
Add x to both sides: 5x=-15
Divide by 5: x=-3

Do the same for the other problems.

Answer 7

y=4x
x=y/4


y=-x-15
y=-y/4-15

y = (-y - 60)/4 (find common denominator)

4y = -y - 60

4y +y =-60

5y = -60

y = -60/5

y = - 12

you can do all the other problems same way.