Question

Solve the simultaneous equations
5x + 6y = 3
2x - 3y = 12

Answer 1

x = 3, y = -2.

Explanation:

5x + 6y = 3

2x - 3y = 12 Multiply this by 2:

4x - 6y = 24 Now add this to the first equation:

9x = 27

x = 3.

Substitute x = 3 in the second equation:

2(3) - 3y = 12

-3y = 12 - 6 = 6

y = 6 / -3

y = -2.

Answer 2

Answer: x =3; y = -2

`\left \{ {{5x+6y=3} \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=(3-6y)/(5) } \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=(3-6y)/(5) } \atop {2.(3-6y)/(5)-3y =12}} \right.\\\\<=>\left \{ {{x=(3-6y)/(5) } \atop {6-12y-15y=12.5}} \right.\\\\<=>\left \{ {{x=(3-6y)/(5) } \atop {17y=6-60=-54}} \right.\\\\<=>\left \{ {{x=(3-6y)/(5) } \atop {y=-54/27}} \right.\\\\\\ <=>\left \{ {{x=(3-6y)/(5) } \atop {y=-2}} \right.\\\\<=>\left \{ {{x=3} \atop {y=-2}} \right.`

Explanation: