How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x-5y= -17 and -2x+y=6?

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Answer 1 · 2018-01-11T19:16:24

$x = -13/2, y = -7$ (one solution)

$8x-5y = -17$
$-2x+y= 6$ (*4)

$8x-5y = -17$
$-8x+4y= 24$

add both together:

$0x -1y = 7$

$-y = 7$

multiply by $-1$ :

$y = -7$

$-2x+y= 6$

substitute $y$ for the value found:

$-2x-7 = 6$

add $7$ :

$-2x = 13$

divide by $2$ :

$x = -13/2$

on a graph, there is only one point of intersection,
at $(-6.5, 7):$
![ desmos.comm