Question

How many solutions does the system of equations x − y = 7 and y equals the square root of the quantity 3 times x plus 3 end quantity minus 2 have?

0
1
2
Infinitely many

Answer 1

Your answer is: 1 solution

Explanation:

To find the solution, we can substitute the value of y from the second equation into the first equation.

x - (√(3x + 3) - 2) = 7

Next, we can solve for x by simplifying the equation.

x - √(3x + 3) + 2 = 7

Then, we can isolate the square root term.

x - √(3x + 3) = 7 - 2

x - √(3x + 3) = 5

Next, we can square both sides of the equation to eliminate the square root.

(x - √(3x + 3))^2 = 5^2

x^2 - 2x√(3x + 3) + 3x + 3 = 25

x^2 + 3x - 2x√(3x + 3) + 3 = 25

Rearranging the terms, we get:

x^2 + 3x - 22 - 2x√(3x + 3) = 0

Now, we can solve for x by factoring, completing the square, or using the quadratic formula. After finding the value of x, we can substitute it back into either of the original equations to find the corresponding value of y.