"Simple" algebra question?

Question

If 2x² + 8y = 121.5 and x² - 8y = 121.5, then x =

Answer 1

start with 2 equations in 2 unknowns

2x^2+8y=121.5

x^2 -8y=121.5

add the 2 equations and we get

3x^2 = 243

x^2 = 81 so x= +9 or -9

We can solve for y by plugging in these values of x in one of the equations . I will strait with the second since it is simpler

(9)^2 -8y= 121.5

81-8y =121.5

8y= 40.5 y= 40.5/8.To see if this is a real or extraneous solution we need to rest if these values hold for the first equation as well

2( 81 ) + 8(40.5/8) = 162 +40.5= 202.5 this does not work since it should equal 121.5

There fore the solution is x=-9 y= 40.5/8

If younplug these values first equation you will get 121.5

Answer 2

This system of nonlinear equations fits into elimination by addition

If you add the two equations together the y is eliminated

2x² + 8y = 121.5

x² - 8y = 121.5

Addition eliminates the y and we have

3x² = 243

Divide both sides by 3 to give

x² = 81

x = ±√81

So x will be the positive and negative square root of 81

x = 9 and x = -9

In order to check this equation you should solve for y; y is -5.0625 this can be found by substituting the values of x in the original equations.

If you choose to solve for y first Substitution works well as well for the system:

2x² + 8y = 121.5

x² - 8y = 121.5

In the second equation, x² = 121.5 + 8y; which can be substituted into the first equation to give

2(121.5 + 8y) + 8y = 121.5

243 + 16y + 8y =121.5

24y = 121.5 - 243

24y = - 121.5

Divide both sides by 24

y = -121.5/24

y = -5.0625

Plug y into the original equations to check the x values we obtained in the elimination above gives:

2x² + 8y = 121.5

x² - 8y = 121.5

2x² + 8(-5.0625) = 121.5

2x² - 40.5 = 121.5

Add 40.5 to both sides

2x² = 121.5 + 40.5

2x² = 162

Divide both sides by 2

x² = 81

x = ±√81

Again x is the positive and negative square roots of 81

x = -9 and x = 9

Checking with the second equation

x² - 8y = 121.5

x² - 8(-5.0625) = 121.5

x² + 40.5 = 121.5

Subtract 40.5 from both sides

x² = 81

x = ±√81

So x is the positive and negative square root of 81

x = -9 and x = 9

I hope you find this useful and please send me a message if you have any questions