solving systems by substitution?

Question

1. y=x^2
y=1/2x+5
2. y=4/x
y=x-3
3. y=root x
y=x-6
4. y=|x|
y=x+2
5. y=|x|
y=1/2x+4

Answer 1

To solve a system means to determine the values of x and y that make both systems true!

To solve by substitution, means to substitute one equation into the other, thus eliminating a variable. Then solve.

I will use your first question as an example.

Equation 1 is y = x^2
Equation 2 is y = (1/2)x + 5

So, set Equation 1 = Equation 2

Thus, x^2 = (1/2)x + 5

Now solve x^2 - (1/2)x - 5 = 0
This is the same as 2x^2 - x - 10 = 0

Using the quadratic formula (or factoring) you get the solutions

x = 2.5 or x = -2

Answer 2

basically you would change x and y such that they can cancel out each other.
you can change x and y by multiplying the entire equation by some
number, here i'lll show you.

number 2) y=4x is the same thing as y=1/4 (x), right?
ok so what you would do to make it like y=x-3 is that you would
multiply y=1/4(x) by 4, giving you 4y = x.
Than if you want to cancel it out, you subtract, for example
4y = x
y = x-3
you would subtract the system of equations
so
4y-y = 3y
x-x = 0
and 0- (-3) = 3
so you would get 3y = 3
and you sovle for y which is 1
than you can solve for x by inputting y.
for example
y=4/x
by inputting 1 for y you get
1 = 4/x, x = 4
so the answer for x is 4

that may seem a bit complicated, but with some practice you should be able to get it! good luck!

Answer 3

You'd isolate the variable from one equation and put it into the other
5. y=1/2x+4
y-4=1/2x
2y-8=x
y=|2y-8|
y+-2y=-8
+) 3y=-8 y=-8/3
-) y=8

4. y=x+2
x=y-2
y=|y-2|
y+-y=-2
+) 2y=-2
y=-1
-) 0=-2 not root