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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When you multiply the numerator and denominator by the same number, you get an equivilent fraction
<span>answer
A) (-5,-49),(-2,-22),(3,23)
</span>when x = - 5 ; y=9x-4 = 9(-5) -4 = -49
when x = - 2 ; y=9x-4 = 9(-2) -4 = -22
when x = 3 ; y=9x-4 = 9(3) -4 = 23
The answer is 8 hoped that help always fell free to comment me if you have any more questions and always good luck
A. 12*x + 2*y = 90
6*x + 2*y = 60
To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.
B. Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5
now we replace x in any of 2 equations to get y.
30+2y = 60
2y = 30
y=15
Solo acts are 5 minutes long and ensemble acts are 15 minutes long
