Asked by Neil
Solve the system of equations by an algebraic method. Leave answer in exact form.
4x² - 7y² = 21
x² + 2y² = 99
4x² - 7y² = 21
x² + 2y² = 99
Answers
Answered by
Ron
4x² - 7y² = 21 (eq1)
x² + 2y² = 99 (eq2)
--> eq1-4*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 =99-50
--> x² =49 (eq5)
x =(+/-)sqrt(49) (eq6)
###############
# x =(+/-)7 # (eq7)
###############
y =(+/-)sqrt(25) (eq8)
###############
# y =(+/-)5 # (eq9)
###############
You could also use Matrix Methods
x² + 2y² = 99 (eq2)
--> eq1-4*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 =99-50
--> x² =49 (eq5)
x =(+/-)sqrt(49) (eq6)
###############
# x =(+/-)7 # (eq7)
###############
y =(+/-)sqrt(25) (eq8)
###############
# y =(+/-)5 # (eq9)
###############
You could also use Matrix Methods
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