algebra 2 math ?

Question

The sum of eight times a number plus three times a larger number is thirteen. The sum of three times the same smaller number and twice the larger number is eleven.

Answer 1

If you want to know what the numbers are, a system of equations in two unknowns will do that

x = smaller number

y = larger number

According to the information given we have

Equation 1

8x + 3y = 13

And

Equation 2

3x + 2y =11

I will solve below by Elimination.

I will multiply Equation 1 by 2 and Equation 2 by negative 3 to eliminate y

2(8x + 3y = 13)

-3(3x + 2y = 11)

To yield

16x + 6y = 26

-9x - 6y = -33

Combining these y is eliminated and we have

7x = -7

Divide both sides by 7

x = -1

Now I will substitute -1 into the original Equation 1 and solve for y

8x + 3y = 13

8(-1) + 3y = 13

-8 + 3y = 13

Add 8 to both sides

3y = 13 + 8

3y = 21

Divide both sides by 3

y = 7

You can check the values in the original equations

8(-1) + 3(7) = 13

-8 + 21 = 13

13 = 13

3x + 2y = 11

3(-1) + 2(7) = 11

-3 + 14 = 11

11 = 11

I hope you find this useful if you any questions please send me a message.