The line passing through the point of intersection of x + y = 2, x - y = 0 and is parallel to x + 2y = 5 is ax + by = c, then value of a + b + c is

Question

The line passing through the point of intersection of $x + y = 2$ , $x - y = 0$ and is parallel to $x + 2 y = 5$ is $a x + b y = c$ , then value of $a + b + c$ is _________.

Smart Achievers · Accepted Answer

(6)

$Required equation of line which is parallel to given line x + 2 y = 5 is x + 2 y + k = 0$ $\dots (i)$

$Given equations of lines are$

$x + y = 2$ $\dots (i i)$

$x - y = 0$ $\dots (i i i)$

$Adding (ii) and (iii), we get 2 x = 2$ $\Rightarrow x = 1$

$Substituting x = 1 in (iii), we get y = 1$

$∴$ $Point of intersection is (1, 1)$

$Substituting x = 1, y = 1 in (i), we get$

$1 + 2 + k = 0$ $\Rightarrow k = - 3$

$∴$ $Required equation of line is x + 2 y = 3$

$Here, a = 1, b = 2 and c = 3$

$∴$ $a + b + c = 1 + 2 + 3 = 6$

Solution

Q.
The line passing through the point of intersection of $x + y = 2$ , $x - y = 0$ and is parallel to $x + 2 y = 5$ is $a x + b y = c$ , then value of $a + b + c$ is _________.

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Solution

Q. The line passing through the point of intersection of x+y=2, x-y=0 and is parallel to x+2y=5 is ax+by=c, then value of a+b+c is _________.

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Q.
The line passing through the point of intersection of $x + y = 2$ , $x - y = 0$ and is parallel to $x + 2 y = 5$ is $a x + b y = c$ , then value of $a + b + c$ is _________.