x = -3
y = -4
Step-by-step explanation:
We're given:
- Two times a number minus four times another number is ten
- Four times the first number minus four times the second number results in four
Let the first number be x and the second be y.
Translate the given information into equations:
- Two times [a number] minus four times [another number] is ten
[tex]2x-4y=10[/tex]
- Four times [the first number] minus four times [the second number] results in four[tex]4x-4y=4[/tex]
Now, solve using elimination:
- [tex]2x-4y=10\\\hspace{5} 4x-4y=4\\\rule{60}{0.3}\\-2x=6[/tex]
Solve for x:
[tex]-2x=6\\x=-3[/tex]
Therefore, the first number is -3.
Now, solve for y using x:
[tex]2x-4y=10\\2(-3)-4y=10\\-6-4y=10\\-4y=16\\y=-4[/tex]
Therefore, the second number is -4.