Algebra
posted by Neil on .
Solve the system of equations by an algebraic method. Leave answer in exact form.
4x²  7y² = 21
x² + 2y² = 99

4x²  7y² = 21 (eq1)
x² + 2y² = 99 (eq2)
> eq14*eq2
>
4x²  7y² = 21 (eq1)
4x²  8y² = 396 4*(eq2)
___________________
15y²=375 (eq3)
> y²=25 (eq4)
Back sub to get
x² + 2(25) = 99
> x² =9950
> x² =49 (eq5)
x =(+/)sqrt(49) (eq6)
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# x =(+/)7 # (eq7)
###############
y =(+/)sqrt(25) (eq8)
###############
# y =(+/)5 # (eq9)
###############
You could also use Matrix Methods