Question

one number is 11 more than another number. find the two number if three times the larger number exceeds four times the smaller number by 4​

Answer 1

Answer:

a = 40

b = 29

Explanation:

Give a place holder for the numbers that we don't know.

Lets call the two numbers a and b.

From the given info, we can write an expression and solve it:

"one number is 11 more than another number"

a = 11 + b

from this, we know that a > b.

''three times the larger number exceeds four times the smaller number by 4"

3a = 4b + 4

Now we have 2 equations, we can use them to solve using whatever method you want.

a = 11 + b

3a = 4b + 4

I will be using matrices RREF to solve for this.

a - b = 11

3a - 4b = 4

$\begin{bmatrix}1 & -1 & 11\\3 & -4 & 4 \end{bmatrix}$

$\begin{bmatrix}1 & 0 & 40\\0 & 1 & 29 \end{bmatrix}$

a = 40

b = 29