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What is the solution of the system $y = x - 10, y = 2 x + 5$ $y=x-10, y=2x+5$ ?

1 Answer

Nov 12, 2016

$x = - 15 and y = - 25$ $x = -15 and y = -25$

Explanation:

This is a perfect scenario for solving the two equations.
(which represent straight lines and the solution gives the point of intersection.)

$y = x - 10 and y = 2 x + 5$ $color(blue)(y = x-10)" and "color(red)(y = 2x+5)$

The two $y -$ $y-$ values are equal!

$\times \times \times \times \times \times x y = y$ $color(white)(xxxxxxxxxxxxx)color(blue)(y) = color(red)(y)$

Therefore: $\times x x - 10 = 2 x + 5$ $color(white)(xxx)color(blue)(x-10) =color(red)(2x+5)$

$\times \times . \times x - 10 - 5 = 2 x - x$ $color(white)(xxxx.xxx)-10-5 =2x-x$

$\times \times . \times x - 15 = x \leftarrow$ $color(white)(xxxx.xxx)-15 =x" "larr$ we have the x-value

$y = (- 15) - 10 = - 25 \leftarrow$ $y = (-15)-10 = -25" "larr$ from the first equation

Check in the second equation:

$y = 2 (- 15) + 5 = - 25$ $y = 2(-15)+5 = -25$

$x = - 15 and y = - 25$ $x = -15 and y = -25$

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