Question

What is the smallest value of y in the solution set to the system of equations below?

y=x^2+6x+23
y=18x-12

Answer 1

The smallest value of y in the given two equations is 78

Explanation:

Given as :

The two equation is given as :

y = x² + 6 x +23 ...........1

y = 18 x - 12. ..........2

Now, solving both equations

putting the value of y from eq 2 into eq 1

So, x² + 6 x +23 = 18 x - 12

Or, x² + 6 x +23 - 18 x + 12 = 0

Or, x² - 12 x + 35 = 0

Or, x² - 5 x - 7 x + 35 = 0

Or, x (x - 5) - 7(x - 5) = 0

Or, (x - 5) (x - 7) = 0

∴ x = 5 , 7

Now, for smallest value of y , take x = 5

∴ put the value of x in eq 2

So, y = 18 x - 12

I.e y = 18 × 5 - 12

Or, y = 90 - 12

∴ y = 78

Hence, The smallest value of y in the given two equations is 78 . answer