Question

Two numbers are related to each other in the following ways.

• The second number is five more than the square of the first number

•The product of triple the first number and three less than the first number is equal to the second number.

How do I solve the system of equations.

Answer 1

Explanation:

Let's call the first number x and the second number y.

From the first statement, we know that:

y = 5 + x^2

From the second statement, we know that:

3x * (x - 3) = y

Substitute the expression for y from the first statement into the second equation:

3x * (x - 3) = 5 + x^2

Expand the left side:

3x^2 - 9x = 5 + x^2

Subtract x^2 from both sides:

2x^2 - 9x - 5 = 0

We can solve for x using the quadratic formula:

x = (9 ± √(9^2 - 4 * 2 * (-5))) / (2 * 2)

x = (9 ± √(97)) / 4

x ≈ 2.34 or x ≈ -1.07

Since we're dealing with real-world numbers, we can ignore the negative solution for x.

Now, we can use the first statement to find y:

y = 5 + x^2

y ≈ 11.16

So the two numbers are approximately 2.34 and 11.16.