Where do the lines $3 x + y = 9$ $3x + y = 9$ and $4 x + 2 y = 6$ $4x + 2y = 6$ intersect?

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Where do the lines $3 x + y = 9$ $3x + y = 9$ and $4 x + 2 y = 6$ $4x + 2y = 6$ intersect?

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Answer 1 · 2017-01-26T04:30:27

The solution is $(6, - 9)$ $(6, -9)$ .

Explanation:

You need to start by isolating one of the variables. Usually, if one of the variables has coefficient $1$ $1$ , then this will be easiest to isolate.

$3 x + y = 9 \to y = 9 - 3 x$ $3x + y = 9 -> y = 9 - 3x$

Substitute this into the other equation now for $y$ $y$ , leaving only x's.

$4 x + 2 (9 - 3 x) = 6$ $4x + 2(9 - 3x) = 6$

$4 x + 18 - 6 x = 6$ $4x + 18 - 6x = 6$

$- 2 x = - 12$ $-2x = -12$

$x = 6$ $x = 6$

Now insert $x = 6$ $x = 6$ into one of the equations to solve for $y$ $y$ .

$3 (6) + y = 9$ $3(6) + y = 9$

$y = 9 - 18$ $y = 9 - 18$

$y = - 9$ $y = -9$

The intersection point of the two lines is therefore $(6, - 9)$ $(6, -9)$ . Remember: when graphing, points are always listed in the form $(x, y)$ $(x, y)$ .

Hopefully this helps!

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Where do the lines $3 x + y = 9$ $3x + y = 9$ and $4 x + 2 y = 6$ $4x + 2y = 6$ intersect?

1 Answer

Explanation:

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