1.
\(8x+5y=6 \ \ \ |\times 2 \\
3x-2y=10 \ \ \ |\times 5 \\ \\
16x+10y=12 \\
\underline{15x-10y=50} \\
16x+15x=12+50 \\
31x=62 \ \ \ |\div 31 \\
x=2 \\ \\
3x-2y=10 \\
3 \times 2-2y=10 \\
6-2y=10 \ \ \ |-6 \\
-2y=4 \ \ \ |\div (-2) \\
y=-2 \\ \\
(x,y)=(2,-2)\)
2.
\(-3x+8y=10 \ \ \ |\times 5 \\
5x+6y=80 \ \ \ |\times 3 \\ \\
-15x+40y=50 \\
\underline{15x+18y=240 \ \ } \\
40y+18y=50+240 \\
58y=290 \ \ \ |\div 58 \\
y=5 \\ \\
5x+6y=80 \\
5x+6 \times 5=80 \\
5x+30=80 \ \ \ |-30 \\
5x=50 \ \ \ |\div 5 \\
x=10 \\ \\
(x,y)=(10,5)\)
3.
\(4x+12y=-24 \\
3x-6y=-18 \ \ \ |\times 2 \\ \\
4x+12y=-24 \\
\underline{6x-12y=-36} \\
4x+6x=-24-36 \\
10x=-60 \ \ \ |\div 10 \\
x=-6 \\ \\
3x-6y=-18 \\
3 \times (-6)-6y=-18 \\
-18-6y=-18 \ \ \ |+18 \\
-6y=0 \ \ \ |\div (-6) \\
y=0 \\ \\
(x,y)=(-6,0)\)
4.
\(5x-6y=48 \ \ \ |\times 2 \\
2x+5y=-3 \ \ \ |\times (-5) \\ \\
10x-12y=96 \\
\underline{-10x-25y=15} \\
-12y-25y=96+15 \\
-37y=111 \ \ \ |\div (-37) \\
y=-3 \\ \\
2x+5y=-3 \\
2x+5 \times (-3)=-3 \\
2x-15=-3 \ \ \ |+15 \\
2x=12 \ \ \ |\div 2 \\
x=6 \\ \\
(x,y)=(6,-3)\)
