What is the solution to the system of equations $y = 2 x - 1$ $y = 2x-1$ and $y = - x + 5$ $y = -x + 5$ ?

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Answer 1 · 2016-01-01T10:55:39

$x = 2, y = 3$ $x=2, y=3$

By elimination:

$y = 2 x - 1$ $y=2x-1$

$2 x - y = 1$ $2x-y=1$ --- $(1)$ $(1)$

$y = - x + 5$ $y=-x+5$

$x + y = 5$ $x+y=5$ --- $(2)$ $(2)$

$(1) + (2) :$ $(1)+(2):$

$2 x - y + x + y = 1 + 5$ $2x-y+x+y=1+5$

$3 x = 6$ $3x=6$

$x = 2$ $x=2$

Subsitute $x = 2$ $x=2$ into $(2)$ $(2)$ :

$2 + y = 5$ $2+y=5$

$y = 3$ $y=3$

What is the solution to the system of equations y=2x−1y = 2x-1 and y=−x+5y = -x + 5?