How do you solve 2x + 3y = 2 and x + 6y = 4?

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Answer 1 · 2018-06-16T12:00:45

See a solution process below:

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

$x + 6y = 4$

$x + 6y - color(red)(6y) = 4 - color(red)(6y)$

$x + 0 = 4 - 6y$

$x = 4 - 6y$

Step 2) Substitute $(4 - 6y)$ for $x$ in the first equation and solve for $y$ :

$2x + 3y = 2$ becomes:

$2(4 - 6y) + 3y = 2$

$(2 xx 4) - (2 xx 6y) + 3y = 2$

$8 - 12y + 3y = 2$

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

$8 + (-9)y = 2$

$8 - 9y = 2$

$8 - color(red)(8) - 9y = 2 - color(red)(8)$

$0 - 9y = -6$

$-9y = -6$

$(-9y)/color(red)(-9) = (-6)/color(red)(-9)$

$y = 2/3$

Step 3) Substitute $2/3$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$ :

$x = 4 - 6y$ becomes:

$x = 4 - (6 xx 2/3)$

$x = 4 - 12/3$

$x = 4 - 4$

$x = 0$

The Solution Is:

$x = 0$ and $y = 2/3$

Or

$(0, 2/3)$