Question

What are the solutions to the following system of equations? x − y = 6 y = x2 −6

Answer 1

The solutions to the given system of equations is (0, -6) and (1, -5)  

Simultaneous equations

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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