The solutions to the given system of equations is (0, -6) and (1, -5)
<h3>Simultaneous equations</h3>
From the question, we are to determine the solutions to the given system of equations
The equations are
x − y = 6 --------- (1)
y = x² −6 ---------- (2)
From equation (1)
x - y = 6
∴ x = 6 + y ------- (3)
Substitute into equation (2)
y = x² −6
y = (6+y)² −6
y = (6+y)(6+y) -6
y = 36 + 6y + 6y +y² -6
y = 36 + 12y + y² - 6
Simplifying
y² + 12y - y + 30 = 0
y² + 11y + 30 = 0
Solve quadratically
y² + 11y + 30 = 0
y² + 6y + 5y + 30 = 0
y(y +6) +5 (y +6) = 0
(y + 5)(y + 6) = 0
y + 5 = 0 OR y + 6 = 0
y = -5 OR y = -6
Substitute the values of y into equation (3)
x = 6 + y
When y = -5
x = 6 + (-5)
x = 6 -5
x = 1
When y = -6
x = 6 + (-6)
x = 6 -6
x = 0
∴ When x = 0, y = -6 and when x = 1, y = -5
Hence, the solutions to the given system of equations is (0, -6) and (1, -5)
Learn more on Solving simultaneous equations here: brainly.com/question/16863577
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Answer:
hypotenuse = 25 yards
Step-by-step explanation:
Use pythagorean theorem
c^2 = a^2 + b^2 where c = hypotenuse and 'a' and 'b' are the legs
hyp^2 = 24^2 + 7^2
hyp^2 = 625
hyp = 25 yd
10.25 + 2.00 = 12.25...cost of pizza and soda
12.25 - 1.50x = 4.75....with x being the number of touchdowns
-1.50x = 4.75 - 12.25...I subtracted 12.25 from both sides
-1.50x = - 7.50...now divide both sides by -1.50
x = -7.50 / -1.50
x = 6......They would have to score 6 touchdowns
