Question

Q8 Q17.) Find the numbers.

Answer 1

Let x = the first number
      y = the second number
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First: set up the equations.

Four times a first number: 4x
Decreased by a second number: - y
Is 4: = 4

4x - y = 4.

The first number increased by: x + 
three times the second number: 3y
is -25: = -25

x + 3y = -25.
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You can make your system of equations now.

4x - y = 4
x + 3y = -25

I would use substitution to solve these.

To do substitution, isolate a variable first, in one of the equations. I would probably isolate x in the second equation.

x + 3y = -25
x = -25 - 3y

Now, you can substitute -25 - 3y into 4x - y = 4, as x.

4x - y = 4
4(-25 - 3y) - y = 4

Now just solve for y.

-100 - 12y - y = 4
-13y = 104
y = -8

Now, you can put -8 as y into one of the original equations, I'll just use 4x - y = 4.

4x -  y = 4
4x - (-8) = 4
4x + 8 = 4
4x = -4
x = -1

So the first number is -1, and the second -2.

Answer 2

let x be 1st no. and y be the 2nd no.

so 4x - y = 4

and x + 3y = -25

re-arrange first eqn y = 4x - 4

substitute y into second eqn

x + 3(4x - 4) = -25

13x - 12 = -25

13x = -13

x = -1

y = 4(-1 - 1) = -8