Home > Algebra > Linear Systems with Multiplication

How do you determine the solution in terms of a system of linear equations for #5x^2+y^2 = 14#, #3x^2 -2y^2 = -15#?

Answer 1

#x=+-1, y= +-3#

Write #x^2=X, y^2=Y#, which would make it a system of linear equations. 5X+Y=14 and 3X-2Y= -15. This can be solved by substituting Y= 14-5X in 3X-2Y= -15 as,

3X -2(14-5X)=-15 13X= 28-15=13, resulting in X=1, and Y=14-5=9.

X=1 and Y=9 would mean #x=+-1, y= +-3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ethan Adkins

To solve the system of linear equations (5x^2 + y^2 = 14) and (3x^2 - 2y^2 = -15), we can use the method of substitution or elimination. First, rearrange one of the equations to solve for one variable in terms of the other, then substitute this expression into the other equation and solve for the remaining variable. Once we have found the values of one variable, we can substitute them back into one of the original equations to find the corresponding values of the other variable. Finally, we verify the solutions by substituting them into both original equations to ensure they satisfy both equations simultaneously.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.