simultaneous equations by the substitution method?

Question

eg. 2y-x= 1
xy+x^2=26

Answer 1

Hi,



If you solve the first equation for x, it becomes x = 2y - 1.



Substituting this expression into the second equation make it y( 2y - 1) + ( 2y - 1)^2 = 26. This multiplies out to

2y^2 - y + 4y^2 - 4y + 1 = 26.

Combining like terms you get 6y^2 - 5y - 25 = 0.

This factors into ( 2y - 5)( 3y + 5) = 0 and will give you 2 values for y, each of which has its own value of x.

The first factor solves and gives y = 5/2. When you plug this back in, you get x = 4.

The second factor gives y = -5/3. When you plug this back in you get x = -13/3.



Your 2 answers are the points (4, 5/2) and ( -13/3, -5/3).

Answer 2

In the first equation, it's quite easy to solve for x, you get x=2y-1



Substitute this x into the second equation:



(2y-1) y + (2y-1)^2 = 26



2y^2 - y + (4y^2 - 4y +1) = 26



Combine like terms



6y^2 -5y +1 = 26



Subtract the 26 over



6y^2 -5y -25 = 0



Solve for y using the quadratic formula. Plug in the y into x=2y-1 to get the value(s) of x.

Answer 3

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Answer 4

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

xy+x^2=26..........(2)



from(1),y=(x+1)/2....(3)

substitute this value into (2)

x(x+1)/2+x^2=26

multiply by 2

x^2+x+2x^2=52

3x^2+x-52=0.......(4)

use the quadratic formula

in order to solve (4)

x={-1+or-sqrt(1+625)}/6

={-1+or-sqrt625}/6=24/6 or -26/6

= 4 or -13/3



when x=4,

substitute into (3)

y=(4+1)/2=5/2

whenx= -13/3

substitute into (3)

y=(-13/3+1)/2= (-10/3)/2

= -5/3



hence,we have solution sets

{4,5/2},{-13/3,-5/3}



i hope that this helps

Answer 5

So you want us to do your homework, huh ?



The substitution method is the way to solve this problem. Get an expression for x in terms of y, or y in terms of x, and plug into the appropriate equation ... then repeat for the other term.



Next time, pay attention in class.

Answer 6

2y-x= 1

2y-1=x

xy+x^2=26

(2y-1)y+(2y-1)^2=26

2y^2-2y+4y^2-4y+1=26

6y^2-6y-25=0

y=(6+/-√(36+4*6*25))/12=.5+/-1/12 √636

y=.5+/-1/6 √159

y=-1.60, 2.60

x=2y-1=-4.20, 4.20



solutions are (-4.20, -1.60), (4.20, 2.60)

Answer 7

2y-x=1

1+x=2y

1/2 +x/2=y

2+2x=y

2x=2y

2/2=x/y

x=1

y=1



could not figure out x variable in second question, x to the power of something?

Answer 8

Please, people. I hate decoding questions. State yourself clearly.



If you are wondering if you can use the substitution method, then the answer is yes, after a little rearranging. I'd tell you in detail, but I have better ways to spend my morning.

Answer 9

y= -25

x = 51

Answer 10

2y-x=1

xy+x^2=26

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

-x=-2y+1

x=2y-1

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

y(2y-1)+(2y-1)^2=26

2y^2-y+4y^2-4y+1=26

6y^2-4y+1=26

6y^2-4y-25=0



......