Answer:
Equation 1: [tex]x+y =23.[/tex]
Equation 2 : [tex]x-y =3.[/tex]
1st number: 13
2nd number: 10
Step-by-step explanation:
Let the first number be x;
x = first number
Let the second number be y;
y = second number
Now Given, Two numbers add up to 23.
Hence the equation can be made as;
[tex]x+y =23.[/tex]
Equation 1: [tex]x+y =23.[/tex]
Also Given, 7 times the difference of the two numbers is 21.
Hence the equation can be made as;
[tex]7(x-y) =21[/tex]
Dividing 7 on both side we get;
[tex]\frac{7(x-y)}{7} =\frac{21}{7}\\\\x-y = 3[/tex]
Equation 2 : [tex]x-y =3.[/tex]
Now we will solve the system of equations we get;
We will add equation 1 and equation 2 we get;
[tex](x+y)+(x-y) =23+3\\x+y+x-y=26\\2x=26\\x = \frac{26}{2}=13[/tex]
1st number: 13
Now Substituting the value of x in equation 1 we get;
[tex]x+y=23\\13+y=23\\y=23-13\\y=10[/tex]
2nd number: 10
Hence Final Answer is.
Equation 1: [tex]x+y =23.[/tex]
Equation 2 : [tex]x-y =3.[/tex]
1st number: 13
2nd number: 10
