How do you solve the system of equations $3 x - 2 y = 7$ $3x-2y=7$ and $x + 3 y = - 5$ $x+3y=-5$ ?

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Answer 1 · 2017-02-02T14:58:29

See the entire solution process below:

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

$x + 3 y = - 5$ $x + 3y = -5$

$x + 3 y - 3 y = - 5 - 3 y$ $x + 3y - color(red)(3y) = -5 - color(red)(3y)$

$x + 0 = - 5 - 3 y$ $x + 0 = -5 - 3y$

$x = - 5 - 3 y$ $x = -5 - 3y$

Step 2) Substitute $- 5 - 3 y$ $-5 - 3y$ for $x$ $x$ in the first equation and solve for $y$ $y$ :

$3 (- 5 - 3 y) - 2 y = 7$ $3(-5 - 3y) - 2y = 7$

$- 15 - 9 y - 2 y = 7$ $-15 - 9y - 2y = 7$

$- 15 - 11 y = 7$ $-15 - 11y = 7$

$15 - 15 - 11 y = 15 + 7$ $color(red)(15) - 15 - 11y = color(red)(15) + 7$

$0 - 11 y = 22$ $0 - 11y = 22$

$- 11 y = 22$ $-11y = 22$

$\frac{- 11 y}{- 11} = \frac{22}{- 11}$ $(-11y)/color(red)(-11) = 22/color(red)(-11)$

$(color(red)(cancel(color(black)(-11)))y)/cancel(color(red)(-11)) = -2$

$y = -2$

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

$x = -5 - (3 xx -2)$

$x = -5 - (-6)$

$x = -5 + 6$

$x = 1$

The solution is $x = 1$ and $y = -2$

How do you solve the system of equations 3x-2y=73x−2y=73x-2y=7 and x+3y=-5x+3y=−5x+3y=-5?