Answer:
y = 14/3 and 2
x = -13/3 and 1
(-13/3, 14/3) and (1, 2)
Step-by-step explanation:
[tex]x + 2y = 5 - - - (a) \\ {x}^{2} - {y}^{2} = - 3 - - - (b)[/tex]
for equation (a)
make x the subject of the formular:
[tex]x = 5 - 2y - - - (c)[/tex]
for equation (b)
[tex] {x}^{2} - {y}^{2} = - 3[/tex]
substitute for x as 5 - 2y in equation (b):
[tex] {(5 - 2y)}^{2} - {y}^{2} = - 3 \\ (25 - 20y + 4 {y}^{2} ) - {y}^{2} = - 3 \\ 25 - 20y + 3 {y}^{2} = - 3 \\ {3y}^{2} - 20y + 28 = 0 \\ (3y - 14)(y - 2) = 0[/tex]
therefore,
[tex]y = \frac{14}{3} \: \: and \: \: 2[/tex]
substitute for all values of y in equation (c):
for y = 14/3:
[tex]x = 5 - 2( \frac{14}{3} ) \\ \\ x = 5 - \frac{28}{3} \\ \\ x = - \frac{13}{3} [/tex]
for y = 2:
[tex]x = 5 - 2(2) \\ x = 5 - 4 \\ x = 1[/tex]
Answer:
(1, 2)
(-13/3, 14/3).
Step-by-step explanation:
x + 2y = 5
x² - y² = -3
From the first equation x = 5 - 2y
Substitute for y in the second equation:
(5 - 2y)^2 - y^2 = -3
25 + 4y^2 - 20y - y^2 = -3
3y^2 - 20y + 28 = 0
Factoring:-
(3y - 14(y - 2) = 0
y = 2, 14/3.
So when y = 2, x = 5 - 2(2) = 1.
When y = 14/3, x = 5 - 2(14/3) = -13/3.
Checking the results in the second equation:
(1, 2):-
1^2 - 2^2 = -3 Correct.
(-13/3, 14/3):-
(-13/3)^2 - (14/3)^2 = -3 Correct.
