Q. 32

Question

Graph each equation of the system. Then solve the system to find the points of intersection.

$\{\begin{cases} 2 y^{2} - 3 x y + 6 y + 2 x + 4 = 0 \\ 2 x - 3 y + 4 = 0 \end{cases}$

Step-by-Step Solution

Verified

Answer

The point of intersection is $(7, 6)$ .

1Step 1. Given information

$\{\begin{cases} 2 y^{2} - 3 x y + 6 y + 2 x + 4 = 0 \\ 2 x - 3 y + 4 = 0 \end{cases}$

2Step 2. Graphing each equation

$2 y^{2} - 3 x y + 6 y + 2 x + 4 = 0$

$2 x - 3 y + 4 = 0$

3Step 3. Calculation of intersection point

$C o n s i d e r, 2 y^{2} - 3 x y + 6 y + 2 x + 4 = 0 . . . . . (1) 2 x - 3 y + 4 = 0 . . . . . (2) s u b t r a c t i n g e q . 2 f r o m e q . 1 w e g e t 2 y^{2} - 3 x y + 9 y = 0 2 y - 3 x + 9 = 0 . . . . (3) N o w m u l t i p l y e q . 2 w i t h 3 a n d e q . 3 w i t h 2 . 6 x - 9 y + 12 = 0 4 y - 6 x + 18 = 0 N o w e l i m i n a t e x t o g e t y y = 6 s u b s t i t u t e y = 6 i n e q . 2 t o g e t x 2 x - 3 (6) + 4 = 0 x = 7$

Q. 31

Q. 33

Other exercises in this chapter

Q. 30

Graph each equation of the system. Then solve the system to find the points of intersection.2x2-xy+y2=8xy=4

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Q. 31

Graph each equation of the system. Then solve the system to find the points of intersection.4x2-3xy+9y2=152x+3y=5

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Q. 33

graph each equation of the system. Then solve the system to find the points of intersection.x2-4y2+7=03x2+y2=31

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Q. 34

Graph each equation of the system. Then solve the system to find the points of intersection.3x2-2y2+5=02x2-y2+2=0

View solution