Answer:
[tex]2x + 3y = -25[/tex]
[tex]x - y = 5[/tex]
Answers: [tex]x = -2, y = -7[/tex]
Step-by-step explanation:
Twice a number x means two times the number, x, which is [tex]2x[/tex]. Three times a number, y, translates to [tex]3y[/tex]. 25 less than zero is -25, so the first expression is [tex]2x + 3y = -25[/tex]. The difference between the two numbers being 5 means that [tex]x - y = 5[/tex] since you're taking y away from x. We now have:
[tex]2x + 3y = -25[/tex]
[tex]x - y = 5[/tex]
What we can do now is find x and y. To do that, let's multiply the second equation by 2 so we can eliminate one variable and solve for the other:
[tex]2x + 3y = -25[/tex]
[tex]2x - 2y = 10[/tex]
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[tex]5y = -35[/tex]
[tex]5y/5 = -35/5[/tex]
[tex]y = -7[/tex]
Now that we know one of the numbers, let's put that number back into one of the original equation:
[tex]x - y = 5[/tex]
[tex]x - (-7) = 5[/tex]
[tex]x + 7 = 5[/tex]
[tex]x = -2[/tex]
Just to check, let's put the numbers back into the equations and see if they're correct:
[tex]2(-2) + 3(-7) = -4 + -21 = -4 - 21 = 25[/tex]
[tex]-2 - -7 = -2 + 7 = 7 - 2 = 5[/tex]
