Question

Elimination method

1) -4x + y = -12
4x + 2y = 6

2) 5x + 2y = 12
-6x - 2y = -14

3) 5x + 4y = 12
7x - 6y = 40

4) 5m + 2n = -8
4m + 3n = 2

Answer 1

`1.)\\ \\\begin{cases}-4x + y = -12\\ 4x + 2y = 6 \end{cases}\\ -------- \\ 3y=-6/:3\\ \\y=-2\\ \\-4x+2=-12\\ \\-4x=-12+2`


`-4x=-10/:(-4)\\ \\x=(10)/(4)\\ \\x=(5)/(2)\\ \\\begin{cases}x=(5)/(2) \\y=-2\end{cases}`




`2.)\\ \\\begin{cases}5x + 2y = 12\\ -6x - 2y = -14 \end{cases}\\ -------- \\ -x=-2/*(-1)\\ \\x=2\\ \\5*2+2y=12`


`10+2y=12 \\2y=12-10\\ \\2y=2/:2\\ \\y=1\\ \\\begin{cases}x=2 \\y=1\end{cases}`




`3.)\\ \\\begin{cases} 5x + 4y = 12/*7\\ 7x - 6y = 40/*(-5) \end{cases}\\ \\\begin{cases} 35x + 28y = 84\\ -35x +30y = -200 \end{cases}\\---------- \\58y=-116/:58\\ \\y=-2`


`5x+4*(-2)=12\\ \\5x-8=12\\ \\5x=12+8\\ \\5x=20/:5\\ \\x=4\\ \\\begin{cases}x=4\\y=-2\end{cases}`




`4)\\ \\\begin{cases}5m + 2n = -8 /*4\\ 4m + 3n = 2/(-5) \end{cases}\\ \\ \begin{cases}20m + 8n = -32\\ -20m -15n = -10 \end{cases}\\------------ \\ -7n=-42/:(-7)\\ \\n=6`


`5m+2*6=-8\\5m+12=-8\\5m=-8-12\\5m=-20/:5\\ \\m=-4\\ \\\begin{cases}n=6\\m=-4\end{cases}`

Answer 2

3y=-6
y=-2
4x+2(-2)=6
4x-4=6
4x=10
x=5/2
(5/2,-2)

-x=-2
x=2
5(2)+2y=12
10+2y=12
2y=2
y=1
(2,1)


35x+28y=84
-35x+30y=-200
58y=-116
y=-2
5x+4(-2)=12
5x-8=12
5x=20
x=4
(4,-2)

20m+8n=-32
-20m-15n=-10
-7n=-42
n=6
5m+2(6)=-8
5m+12=-8
5m=-20
m=-4
(-4,6)