f.4 maths.聯立方程

{y=x^2----------(1)
{y=2x-----------(2)
put (1)into (2)
x^2=2x
x^2-2x=0
x(x-2)=0
x=0 or x-2=0
x=0 or x=2
put x=0 into (2)
y=2(0)
y=0
put x=2 into (2)
y=2(2)
y=4

{x^2+y=25--------------(1)
{y=8x+41---------------(2)
put (2)into (1)
x^2+8x+41=25
x^2+8x+41-25=0
x^2+8x+16=0
(x+4)(x+4)
so, x+4=0
x= -4
put x= -4 into (2)
y=8(-4)+41
y=-32+41
y=9

{y=7-4x---------------(1)
{2x^2+y=5-----------(2)
put (1)into (2)
2x^2+7-4x=5
2x^2-4x+7-5=0
2x^2-4x+2=0
(2x-2)(x-1)=0
2x-2=0 or x-1=0
2x=2 or x=1
x=1 or x=1
so , x=1
put x=1 into (1)
y=7-4(1)
y=7-4
y=3

{x^2=2y-----------------(1)
{2y=4x+5----------------(2)
put (1) into (2)
x^2=4x+5
x^2-4x-5=0
(x+1)(x-5)=0
x+1=0 or x-5=0
x= -1 or x=5
put x= -1 into (2)
2y=4(-1)+5
2y= -4+5
2y=1
y=1/2
put x=5 into (2)
2y=4(5)+5
2y=20+5
2y=25
y=25/2

{y-11=x^2-6x----------(1)
{x+y=5-----------------(2)
from (2)
y=5-x -----------------(3)
put (3) into (1)
5-x-11=x^2-6x
x^2-6x+x+6=0
x^2-5x+6=0
(x-2)(x-3)=0
x-2=0 or x-3=0
x=2 or x=3
put x=2 into (3)
y=5-2
y=3
put x=3 into (3)
y=5-3
y=2

{2x^2+3y=28-----------------(1)
{2x+3y=4--------------------(2)
from (2)
2x+3y=4
3y=4-2x
y=(4-2x)/3 ------------------(3)
put (3) into (1)
2x^2+3(4-2x)/3=28
2x^2+4-2x-28=0
2x^2-2x-24=0
x^2-x-12=0
(x-4)(x+3)=0
x-4=0 or x+3=0
x=4 or x= -3
put x=4 into (3)
y=(4-2*4)/3
y=(4-8)/3
y= -4/3
put x= -3 into (3)
y=[4-2(-3)]/3
y=(4+6)/3
y=10/3

only can help you these six questions~

{y=x^2
{y=2x
x^2=2x
x=2 V 0

{y=x^2-4x
{y=-6
x^2-4x+6=0(捨去)


{x^2+y=25
{y=8x+41
-x^2+25=8x+41
x=-4

{y=7-4x
{2x^2+y=5
7-4x=-2x^2+5
x=1

{y-x^2=16
{y=2x-1
x^2-2x+17=0(捨去)

{x^2=2y
{2y=4x+5
x^2/2=4x+5/2
x=5V-1

{y-11=x^2-6x
{x+y=5
x^2-6x+11=5-x
x=6V-1

{2x^2+3y=28
{2x+3y=4
(28-2x^2)/3=(4-2x)/3
x=-3V4