Respuesta :
Answer:
First number = 3
Second number = 7
Step-by-step explanation:
Let one number be = [tex]x[/tex]
Let other number be = [tex]y[/tex]
"One number added to three times another number is 24" can be written mathematically as:
[tex]x+3y=24[/tex]
Five times the first number added to three times the other number is 36 can be written mathematically as:
[tex]5x+3y=36[/tex]
So, we have a system of equation as:
A) [tex]x+3y=24[/tex]
B) [tex]5x+3y=36[/tex]
Solving for [tex]x[/tex] and [tex]y[/tex] using elimination.
Multiplying equation A with -1 and adding it to B to eliminate [tex]y[/tex]
[tex]-1A[/tex] would be
[tex]-1(x+3y=24)[/tex]
[tex]-x-3y=-24[/tex]
[tex]-1A+B[/tex] would be
[tex]-x-3y=-24[/tex]
+ [tex]5x+3y=36[/tex]
We have,
[tex]5x-x+3y-3y=36-24[/tex]
Thus [tex]y[/tex] is eliminated. Now, we can solve for [tex]x[/tex]
[tex]4x=12[/tex]
Dividing both sides by 4.
[tex]\frac{4x}{4}=\frac{12}{4}[/tex]
∴ [tex]x=3[/tex]
Plugging in [tex]x=3[/tex] in equation A to solve for [tex]y[/tex]
[tex]3+3y=24[/tex]
Subtracting both sides by 3.
[tex]3+3y-3=24-3[/tex]
[tex]3y=21[/tex]
Dividing both sides by 3.
[tex]\frac{3y}{3}=\frac{21}{3}[/tex]
∴ [tex]y=7[/tex]
So, first number = 3
Second number = 7
