How do you solve the system $x-2y=3$ and $4x-8y=12$ using substitution?

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Answer 1 · 2018-06-03T22:28:01

See a solution process below:

Step 1) Solve the first equation for $x$ :

$x - 2y = 3$

$x - 2y + color(red)(2y) = 3 + color(red)(2y)$

$x - 0 = 3 + 2y$

$x = 3 + 2y$

Step 2) Substitute $(3 + 2y)$ for $x$ in the second equation and solve for $y$ :

$4x - 8y = 12$ becomes:

$4(3 + 2y) - 8y = 12$

$(4 * 3) + (4 * 2y) - 8y = 12$

$12 + 8y - 8y = 12$

$12 + 0 = 12$

$12 = 12$

This indicates there is an infinite number of solutions because these lines are in fact the same line.

How do you solve the system x-2y=3x-2y=3 and 4x-8y=124x-8y=12 using substitution?