Final answer:
To find the numbers that satisfy the given equations, we set up a system of equations and solve for the variables. By using the elimination method, we find that the first number is approximately 5.5 and the second number is -1.25.
Step-by-step explanation:
To find the numbers that satisfy the given equations, we can set up a system of equations and solve for the variables. Let's assign the first number as 'x' and the second number as 'y'.
The given equations are:
7x + 6y = 31
3x - 10y = 29
We can solve this system of equations using any method such as substitution, elimination, or graphing. Here, we'll use the elimination method. By multiplying the first equation by 3 and the second equation by 7, we can eliminate 'x' when we add them:
21x + 18y = 93
21x - 70y = 203
By subtracting the second equation from the first one, we get:
(21x + 18y) - (21x - 70y) = 93 - 203
88y = -110
Dividing both sides by 88, we find that 'y' is equal to -1.25.
Substituting this value back into either of the original equations, we can solve for 'x'. Let's use the first equation:
7x + 6(-1.25) = 31
7x - 7.5 = 31
7x = 38.5
Dividing both sides by 7, we find that 'x' is approximately 5.5.
Therefore, the first number is 5.5 and the second number is -1.25.