How do you solve 9x + 2y = 5 and y - 2x + 3 = 0?

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Answer 1 · 2016-12-23T00:44:09

$x = \frac{11}{13}$ $x = 11/13$ and $y = - \frac{17}{13}$ $y = -17/13$

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

$y - 2 x + 3 + 2 x - 3 = 0 + 2 x - 3$ $y - 2x + 3 + color(red)(2x - 3) = 0 + color(red)(2x - 3)$

$y - 2 x + 2 x + 3 - 3 = 0 + 2 x - 3$ $y - 2x + color(red)(2x) + 3 - color(red)(3) = 0 + 2x - 3$

$y - 0 + 0 = 2 x - 3$ $y - 0 + 0 = 2x - 3$

$y = 2 x - 3$ $y = 2x - 3$

Step 2) Substitute $2 x - 3$ $2x - 3$ for $y$ $y$ in the first equation and solve for $x$ $x$ :

$9 x + 2 (2 x - 3) = 5$ $9x + 2(color(red)(2x - 3)) = 5$

$9 x + 4 x - 6 = 5$ $9x + 4x - 6 = 5$

$(9 + 4) x - 6 = 5$ $(9 + 4)x - 6 = 5$

$13 x - 6 = 5$ $13x - 6 = 5$

$13 x - 6 + 6 = 5 + 6$ $13x - 6 + color(red)(6) = 5 + color(red)(6)$

$13 x - 0 = 11$ $13x - 0 = 11$

$13 x = 11$ $13x = 11$

$\frac{13 x}{13} = \frac{11}{13}$ $(13x)/color(red)(13) = 11/color(red)(13)$

$(color(red)(cancel(color(black)(13)))x)/color(red)(cancel(color(black)(13))) = 11/13$

$x = 11/13$

Step 3) Substitute $11/13$ for $x$ in the solution to the second equation in Step 1) and calculate $y$ :

$y = 2(color(red)(11/13)) - 3$

$y = 22/13 - 3$

$y = 22/13 - (3 * 13/13)$

$y = 22/13 - 39/13$

$y = -17/13$