數學題---消元法(15點)求式同答案

代入消元法:
1.{x+y=9---1
{4x+y=6---2
From 1, x=9-y---3
Sub. 3 into 2,
36-4y+y=6
-3y=-30
y=10
Sub. y=10 into 3, x=9-10=-1
∴x=-1, y=10
2.{x-3y=4---1
{2x+3y=8---2
From 1, x=4+3y---3
Sub. 3 into 2,
8+6y+3y=8
9y=0
y=0
Sub. y=0 into 3, x=4+3(0)=4
∴x=4, y=0
3.{x+3y=0---1
{3y-x=4---2
From 1, x=-3y---3
Sub. 3 into 2,
3y-(-3y)=4
6y=4
y=2/3
Sub. y=2/3 into 3, x=-3(2/3)=-2
∴x=-2, y=2/3
4.{4x+3y-7=0---1
{2x-5y+3=0---2
From 1, x=(7-3y)/4---3
Sub. 3 into 2,
(7-3y)/2-5y+3=0
7-3y-10y=-6
-13y=-13
y=1
Sub. y=1 into 3, x=(7-3(1))/4=1
∴x=1, y=1
加減消元法:
1.{4x+y=-3---1
{-3x+2y=5---2
From 1, 8x+2y=-6---3
2-3, -3x-8x=5-(-6)
-11x=11
x=-1
Sub. x=-1 into 1, 4(-1)+y=3
y=7
∴x=-1, y=7
2.{-4x+3y=2---1
{8x-5y=-2---2
From 1, -8x+6y=4---3
2+3, --5y+6y=2
y=2
Sub. y=2 into 1, -4x+2=3
x=-1/4
∴x=-1/4, y=2
3.2x-y=3y-5x=1
{2x-y=1---1
{3y-5x=1---2
From 1, 6x-3y=3---3
3+2, x=2
Sub. x=2 into 1, 2(1)-y=1
y=1
∴x=2, y=1
4.5x+y=11x-5y=12
{5x+y=12---1
{11x-5y=12---2
From 1, 25x+5y=60---3
3+2, 36x=72
x=2
Sub. x=2 into 1, 5(2)+y=12
y=2
∴x=2, y=2
用代入消元法/加減消元法(混合):
1.{3x+y=7---1
{2y=6x-18---2
From 1,y=7-3x---3
Sub. 3 into 2,
14-6x=6x-18
-12x=-32
x=8/3
Sub. x=8/3 into 3, y=7-3(8/3)=-1
∴x=8/3, y=-1
2.{3x-4y=11---1
{5x-2y=7---2
From 1, 10x-4y=14---3
1-3, 7x=3
x=7/3
Sub. x=7/3 into 2, 5(7/3)-2y=7
-2y=-14/3
y=-7/3
∴x=7/3, y=-7/3