If $u = 2 x + 4 y a n d v = x - 3 y + 5$ , find the point of intersection of $77 u - 89 v = 0$ and $87 u + 98 v = 0$ .

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Solution

$u = 2 x + 4 y$ and $v = x - 3 y + 5$
$77 u - 89 v = 0 ⟹ 65 x + 575 y - 445 = 0$
$87 u + 98 v = 0 ⟹ 272 x + 54 y + 490 = 0$
Solving the above two equations we get
$\frac{x}{305780} = \frac{y}{152890}$
$x = 305780$ and $y = 152890$

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If u=2x+4y and v=x−3y+5, find the point of intersection of 77u−89v=0 and 87u+98v=0.

u=2x+4y and v=x−3y+577u−89v=0⟹65x+575y−445=087u+98v=0⟹272x+54y+490=0Solving the above two equations we getx305780=y152890x=305780 and y=152890

If $u = 2 x + 4 y a n d v = x - 3 y + 5$ , find the point of intersection of $77 u - 89 v = 0$ and $87 u + 98 v = 0$ .

$u = 2 x + 4 y$ and $v = x - 3 y + 5$
$77 u - 89 v = 0 ⟹ 65 x + 575 y - 445 = 0$
$87 u + 98 v = 0 ⟹ 272 x + 54 y + 490 = 0$
Solving the above two equations we get
$\frac{x}{305780} = \frac{y}{152890}$
$x = 305780$ and $y = 152890$