Where do the lines $3 x + 5 y = 78$ $3x+5y=78$ and $2 x - y = 0$ $2x-y=0$ intersect?

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Answer 1 · 2017-09-13T22:10:19

lines intersect at $(6, 12)$ $( 6 , 12 )$

If we equate one of the equations with the other, this will allow us to find a point or points that are common to both.

Rearrange both equations so they are in terms of y.

$y = 2 x$ $y = 2x$

$y = - \frac{3}{5} x + \frac{78}{5}$ $y = -3/5x + 78/5$

This leads to:

$2 x = - \frac{3}{5} x + \frac{78}{5}$ $2x = -3/5x + 78/5$

Solving for $x$ $x$ :

Multiplying both sides by $5$ $5$

$10 x = - 3 x + 78$ $10x = -3x + 78$

Adding $3 x$ $3x$ to both sides:

$13 x = 78 \Rightarrow x = 6$ $13x = 78 => x = 6$

Plugging $6$ $6$ into the equation $y = 2 x$ $y = 2x$ :

$y = 2 (6) \Rightarrow y = 12$ $y = 2(6) => y = 12$

So lines intersect at $(6, 12)$ $( 6 , 12 )$

Graph:

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Where do the lines 3x+5y=783x+5y=78 and 2x−y=02x-y=0 intersect?