The sum of twice a larger number, x, and three times a smaller number, y, is 25 less than zero. The difference between the larger number and the smaller number is 5. Which system of equations could be used to find the value of x and y?

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]-----------------------------[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]