How do you solve the following system using substitution?: $4x + 5y = 6, y = 2x - 10$

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Answer 1 · 2015-10-22T10:44:23

$x=4$ , $y=-2$ .

From the second equation, we know that $y=2x-10$ . So we can susbtitute every occurrence of $y$ with $2x-10$ in the first equation:

$4x+5color(green)(y)=6 -> 4x+5color(green)((2x-10))=6$ .

Expanding, we have $4x+10x-50=6$ . Isolating the $x$ term, we have

$14x = 56$ , which we solve for $x$ finding $x= 56/14=4$ .

Once we know the value of $x$ , we obtain $y$ by substituing in the second equation (for example):

$y=2x-10 -> y=2*4-10 = -2$ .

Note that we could have chosen the first equation:

$4x+5y=6 -> 4*4+5y=6 -> 5y=-10 -> y=-2$ .

How do you solve the following system using substitution?: 4x + 5y = 6, y = 2x - 104x + 5y = 6, y = 2x - 10