# How do you solve the following system: x-4y=2, x-2y=4 ?

Mar 4, 2018

$x = 6$
$y = 1$

#### Explanation:

We set up the two equations with 'matching' components and then use algebra to reduce the terms to a solution (if there is one).

1) x − 4y = 2
2) x − 2y = 4 Subtract 1) from 2)

$2 y = 2$ ; $y = 1$ Put this into 1) to find x:

x − 4(1) = 2 ; $x = 6$ Put this back into 2) to check for validity.

6 − 2(1) = 4 ; $6 = 6$ CORRECT!

Mar 4, 2018

$x = 6 , y = 1$

#### Explanation:

$x - 2 y = 4$

$x = 2 y + 4$...........................eq.(1)

$x - 4 y = 2$

$x = 4 y + 2$...........................eq.(2)

$x = x$

eq(1)=eq(2)

$2 y + 4 = 4 y + 2$

$2 y = 2$

$y = 1$

$x - 2 \left(1\right) = 4$

$x = 6$

Mar 4, 2018

$x = 6$, $y = 1$

#### Explanation:

$x - 4 y = 2$

solve for $x$

$x = 2 + 4 y$

*substitute $x$ in the second equation *

$2 + 4 y - 2 y = 4$

$2 + 2 y = 4$

$2 y = 2$

$y = 1$

Now we solve for $x$

$x = 2 + 4 \left(1\right)$

$x = 2 + 4$

$x = 6$

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To double-check, let's plug in our values to the second equation

x−2y=4

$6 - 2 \left(1\right) = 4$

$6 - 2 = 4$

$4 = 4$

We were right!