Question

The sum of two numbers is 18. Twice the first number plus three times the second number equals 40. Find the numbers.

Answer 1

`\left \{ {{x+y=18\:(I)} \atop {2x+3y=40\:(II)}} \right.`
simplify by (-2) first equation

`\left \{ {{x+y=18\:(-2)} \atop {2x+3y=40\:\:\:\:}} \right.`

`\left \{ {{-\diagup\!\!\!\!\!2x-2y=-36} \atop {\diagup\!\!\!\!\!2x+3y=40}} \right.`

`\left \{ {{-2y=-36} \atop {3y=40}} \right.`

`\boxed{\boxed{y = 4}} \end{array}}\qquad\quad\checkmark`

Replace the found value of "y" in the first equation.

`x+y=18\:(I)`

`x + 4 = 18`

`x = 18 - 4`

`\boxed{\boxed{x = 14}} \end{array}}\qquad\quad\checkmark`