Question #1622e

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Answer 1 · 2018-02-14T18:13:42

$x = 7$ $x = 7$ and $y = 6$ $y = 6$

If you like point form, it is: $(7, 6)$ $(7,6)$

Given:

$2 x + y = 20 [1]$ $2x+y=20" [1]"$
$6 x - 5 y = 12 [2]$ $6x-5y=12" [2]"$

We can use equation [1] to write y in terms of x by subtracting 2x from both sides:

$y = 20 - 2 x [1.1]$ $y=20-2x" [1.1]"$
$6 x - 5 y = 12 [2]$ $6x-5y=12" [2]"$

Substitute the right side of equation [1.1] for y in equation [2]:

$6 x - 5 (20 - 2 x) = 12 [2.1]$ $6x-5(20-2x)=12" [2.1]"$

Solve for the value of x:

$6 x - 100 + 10 x = 12 [2.1]$ $6x-100+10x=12" [2.1]"$

$16 x = 112$ $16x = 112$

$x = 7$ $x = 7$

We can use either equation [1] or [2] to find the corresponding value of y; I shall use equation [1]:

$2 (7) + y = 20$ $2(7)+y = 20$

$y = 6$ $y = 6$

Verify that the point $(7, 6)$ $(7,6)$ satisfies both equations:

$2 (7) + 6 = 20$ $2(7)+6=20$
$6 (7) - 5 (6) = 12$ $6(7)-5(6)=12$

$20 = 20$ $20 = 20$
$12 = 12$ $12=12$

Verified