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Let's solve both of these for y and then use the transitive property that will allow us to set them equal to each other.  Solving the first equation for y: [tex]-y=-10 x^{2} +48[/tex] and [tex]y=10 x^{2} -48[/tex].  Now let's work on the second one: [tex]y=8 x^{2} +24[/tex].  If the first equation equals y and the second equation also equals y, then the first equation equals the second equation (that's the transitive property of equality).  [tex]8 x^{2} +24=10 x^{2} -48[/tex]. Simplifying by combining like terms gives us [tex]2 x^{2} =72[/tex] and [tex] x^{2} =36[/tex].  This means that x = 6, -6.  When x = 6, then [tex]y=8(6) ^{2} +24[/tex] and y = 312.  This holds true for both x values because squaring a negative number will give you a positive number.  So the solution sets are (6, 312) and (-6, 312)

The solution of the given system are (6,312) and (-6,312).

What is equation?

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Given that system of equations

10x²- y = 48

2y = 16x²+48

From first equation,  

10x²-y=48

Rewrite the equation as:

y = 10x² - 48

Substitute the value of y in equation 2y = 16x²+48

So, 2(10x² - 48) = 16x²+48

20x² - 96 = 16x²+48

20x² - 16x² = 48 + 96

4x² = 144

x² = 144/4

x² = 36

x = ±6

x = 6, -6

Substitute the value of x = 6 in equation 2y = 16x²+48

2y = 16x²+ 48

2y = 16(6)²+ 48

2y = 16(36)+ 48

2y = 576+ 48

2y = 624

y = 312

Substitute the value of x = -6 in equation 2y = 16x²+48

2y = 16x²+ 48

2y = 16(-6)²+ 48

2y = 16(36)+ 48

2y = 576+ 48

2y = 624

y = 312

Hence, the solution of the given system are (6,312) and (-6,312).

Learn more about equation here:

brainly.com/question/10413253

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