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How do you solve $y = 5 x - 10$ $y = 5x - 10$ and $y = 3 x + 8$ $y = 3x + 8$ using substitution?

1 Answer

Feb 5, 2017

$(x, y) = (9, 35)$ $(x,y)=(9,35)$
(see below for methodology)

Explanation:

Given
[1] $XXX y = 5 x - 10$ $color(white)("XXX")y=5x-10$
[2] $XXX y = 3 x + 8$ $color(white)("XXX")y=3x+8$

Using [1] we can substitute $5 x - 10$ $5x-10$ for $y$ $y$ in [2]
[3] $XXX 5 x - 10 = 3 x + 8$ $color(white)("XXX")5x-10=3x+8$

Simplifying:
[4] $XXX 2 x = 18$ $color(white)("XXX")2x=18$

[5] $XXX x = 9$ $color(white)("XXX")x=9$

We can now use [5] to substitute $9$ $9$ for $x$ $x$ in [1]
[6] $XXX y = 5 \cdot (9) - 10$ $color(white)("XXX")y=5 * (9)-10$

Simplifying
[7] $XXX y = 35$ $color(white)("XXX")y=35$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We could (and should) verify this result by substituting
$x = 9$ $x=9$ and $y = 35$ $y=35$ in [2]
$XXX 35 = 3 \cdot (9) + 8$ $color(white)("XXX")35 = 3 * (9) + 8$ (correct)

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