How do you solve $2 x - y = 3$ $2x-y=3$ and $x + 2 y = 24$ $x+2y=24$ using substitution?

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How do you solve $2 x - y = 3$ $2x-y=3$ and $x + 2 y = 24$ $x+2y=24$ using substitution?

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Answer 1 · 2018-03-30T00:13:23

$2 x - y = 3$ $2x - y = 3$
$x + 2 y = 24$ $x + 2y = 24$

Substitution is a method for solving algebraic equations by finding the value of a variable in terms of other variables and substituting that value into existing equations.
$x = 24 - 2 y$ $x = 24 - 2y$

Substituting $24 - 2 y$ $24 - 2y$ for $x$ $x$ in the first equation:

$2 (24 - 2 y) - y = 3$ $2(24-2y) - y = 3$
$48 - 4 y - y = 3$ $48 -4y - y = 3$
$5 y = 48 - 3$ $5y = 48-3$
$5 y = 45$ $5y =45$
$y = 9$ $y = 9$

Substituting $9$ $9$ for $y$ $y$ in the second equation:
$x + 2 \cdot 9 = 24$ $x + 2*9 = 24$
$x = 24 - 18$ $x = 24 - 18$
$x = 6$ $x = 6$

Answer 2 · 2018-03-30T00:18:02

$x = 6$ $x=6$ and $y = 9$ $y=9$ .

Explanation:

$2 x - y = 3 (1)$ $2x-y=3" " " "(1)$
$x + 2 y = 24 (2)$ $x+2y=24" " " "(2)$

From eqn $(2)$ $(2)$

$x = 24 - 2 y (3)$ $x=24-2y" " " "(3)$

Sub eqn $(3)$ $(3)$ into eqn $(1)$ $(1)$

$2 (24 - 2 y) - y = 3$ $2(24-2y)-y=3$

$48 - 4 y - y = 3$ $48-4y-y=3$

$45 = 5 y$ $45=5y$

$y = 9$ $y=9$

Sub $y = 9$ $y=9$ into eqn $(2)$ $(2)$

$x = 24 - 2 (9)$ $x=24-2(9)$

$x = 6$ $x=6$

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How do you solve $2 x - y = 3$ $2x-y=3$ and $x + 2 y = 24$ $x+2y=24$ using substitution?

2 Answers

Explanation:

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