Find the intersection point of the following lines
$x + y = 4; 2 x - 5 y = 1$

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Solution

$x + y = 4 \dots (1) \times 2$

$2 x - 5 y = 1 \dots (1)$

$\Rightarrow 2 x + 2 y = 8$
$(-) 2 x - 5 y = 1$
____________________
$7 y = 7 \Rightarrow y = 1$

$x + y = 4$ $\Rightarrow x = 4 - y = 3$ $\Rightarrow x = 3$

$∴$ the lines intersect at $(x, y) = (3, 1)$

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Similar questions

Q. Solve the following simultaneous equations.

(i) x + y = 4; 2x

-

5y = 1

Q. Solve the following sets of simultaneous equations.

x + y = 4; 2 x - 5 y = 1

Q. Evaluate:

x + y = 4; 2 x - 5 y = 1

Solve the following sets of simultaneous equations.

(i) x + y = 4 ; 2x

-

5y = 1

(ii) 2x + y = 5; 3x

-

y = 5

(iii) 3x

-

5y =16; x

-

3y = 8

(iv) 2y

-

x =0; 10x + 15y = 105

(v) 2x + 3y + 4 = 0; x

-

5y = 11

(vi) 2x

-

7y = 7; 3x + y = 22

Examine whether the following system is consistent or inconsistent and if consistent find the complete solution
$x + y + z = 4; 2 x + 5 y - 2 z = 3; x + 7 y - 7 z = 5$

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Find the intersection point of the following linesx+y=4;2x−5y=1

x+y=4…(1)×22x−5y=1…(1)⇒2x+2y=8(−)2x−5y=1____________________ 7y=7⇒y=1x+y=4 ⇒x=4−y=3 ⇒x=3∴ the lines intersect at (x,y)=(3,1)

Find the intersection point of the following lines
$x + y = 4; 2 x - 5 y = 1$

$x + y = 4 \dots (1) \times 2$

$2 x - 5 y = 1 \dots (1)$

$\Rightarrow 2 x + 2 y = 8$
$(-) 2 x - 5 y = 1$
____________________
$7 y = 7 \Rightarrow y = 1$

$x + y = 4$ $\Rightarrow x = 4 - y = 3$ $\Rightarrow x = 3$

$∴$ the lines intersect at $(x, y) = (3, 1)$