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Seven times the first number plus six times the second number equals 31.


- Three times the first number minus ten times the second number is 29.

WHAT ARE THE TWO NUMBERS

Respuesta :

For the first equation it should be 1 and 4 because 7(1)+6(4) would simplify to 7+24 which equals 31.

Then for the second equation, well... there’s multiple answers:

First would be 3 and -2 because 3(3)-10(-2) simplifies to 9+20=29.

Another one would be 23 and 4 because 3(23)-10(4) simplifies to 69-40=29.

Hopefully this helps :D
deepakrai138

The first number will be [tex]\frac{11}{2}[/tex] and the second number will be [tex]-\frac{5}{4}[/tex].

Let the first number be x and the second number be y.

According to the question,

Since seven times the first number plus six times the second number equals 31. So,

[tex]7x+6y=31.......(1)[/tex]

Similarly,Three times the first number minus ten times the second number is 29.So,

[tex]3x-10y=29.......(2)[/tex]

Multiplying equation (1) by 3 and equation (2) by 7, we get

[tex]21x+18y=93[/tex]

[tex]21x-70y=203[/tex]

Now subtracting both the equations we get,

[tex]88y=-110[/tex]

[tex]y=-\dfrac{110}{88}[/tex]

[tex]y=-\dfrac{5}{4}[/tex]

putting the value of x in equation (1) we get,

[tex]7x+6\times-\dfrac{5}{4} =31[/tex]

[tex]7x-\dfrac{15}{2}=31\\[/tex]

[tex]7x=31+\dfrac{15}{2}[/tex]

[tex]7x=\dfrac{77}{2}[/tex]

[tex]x=\dfrac{11}{2}[/tex]

Hence the first number is [tex]\frac{11}{2}[/tex] and the second number is [tex]-\frac{5}{4}[/tex].

For more details on solving linear equation in two variables follow the link:

https://brainly.com/question/10270150

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