system equation?

Question

solve

x^ 2+y^2=10
x-2y=1

show working please

Answer 1

Okay, same principle as last time.

Solve for y in the easier equation (x-2y=1)
x-2y=1
x=1+2y

Now we have a value that we can plug into the other equation.
x^2+y^2=10

Plug in x
(1+2y)^2+y^2=10

Expand
1+4y+4y^2+y^2=10

Combine like terms (in this case y^2)
5y^2+4y+1=10

Now bring the 10 over by subtracting 10 on both sides
5y^2+4y-9=0

Factor this equation
(5y+9)(y-1)=0

Since one of these factors must be zero for the whole thing to equal 0,
y=1 and -9/5


Plug each one into the other equation:
x-2y=1
x-2(1)=1

Simplify and solve
x-2=1
x=3

BUT, we have the other solution so you need to plug that one in as well.

x-2y=1
x-2(-9/5)=1
x+18/5=1

Subtract 18/5 from both sides
x=1-18/5
x=5/5-18/5
x=-13/5=-2.6


x=3 and -2.6 or -13/5
y=1 or -9/5

Those are your two answers.

Hope this helps.

Note: the y=1 is paired with the x=3 (3,1) and the y=-9/5 is paired with the x=-13/5 (-9/5, -13/5)

Answer 2

x² + y² = 10- - - - - -Equation 1
x - 2y = 1- - - - - - - Equation 2
- - - - - - - -

Substitute method equation 2

x - 2y = 1
x - 2y + 2y = 1 + 2y

x = 1 + 2y

The answer is x = 1 + 2y

Insert the x value into equation 1

x² + y² = 10

(1 + 2y)² + y² = 10

(1 + 2y)(1 + 2y) = 1 + 2y 2y + 4y² = 1 + 4y + 4y²

1 + 4y + 4y² + y² = 10

1 + 4y + 5y² = 10

1 + 4y + 5y² - 10 = 10 - 10

4y + 5y² - 9 = 0

(5y + 9)(y - 1) = 0

y = 1

Y = - 9/5

Insert the y value into equation 2

- - - - - - - - - - -

x - 2y = 1

x - 2(1) = 1

x - 2 = 1

x - 2 + 2 = 1 + 2

x = 3

The answer x = 3

Insert the x value into equation 1

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


Check for equation 2

x = 2y = 1

3 - 2(1) = 1

3 - 2 = 1

1 = 1

- - - - - - - - - - -

Check for equation 1

x² + y² = 10

(3)² + (1)² = 10

9 + 1 = 10

10 = 10

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

The solution set is { 1, 3 }

or

The solution set is (1, - 1.8)

The y value of y = - 9/5 works

- - - - - - - s-

Answer 3

x^ 2+y^2=10
x-2y=1

x = 2y + 1

plug x into the first equation

(2y+1)^2 + y^2 = 10

4y^2 + 4y + 1 + y^2 = 10
5y^2 + 4y - 9 = 0

use the quadratic equation
a = 5
b = 4
c = -9

y = 1, -1.8

x-2y=1
x - 2(1) = 1
x = 3

x - 2y = 1
x - 2(-1.8) = 1
x = 4.6

ANSWER
(4.6, -1.8)
(3, 1)

Answer 4

Okay, now you may do your own homework. I already helped you with one problem, now you can go through and actually try for yourself. This level of math is extremely easy and these problems should take you about a minute. If you need help, as your teacher for some review problems, or before school help. Getting answers from people online will never truly teach you unless you try for yourself.