How do solve the following linear system?: $x + 2 y = 2, 5 x - 3 y = - 29$ $x+2y =2 , 5x - 3y = -29$ ?

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Answer 1 · 2017-02-20T15:26:43

See the entire solution process below:

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

$x + 2 y = 2$ $x + 2y = 2$

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

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

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

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

$5 x - 3 y = - 29$ $5x - 3y = -29$ becomes:

$5 (2 - 2 y) - 3 y = - 29$ $5(2 - 2y) - 3y = -29$

$10 - 10 y - 3 y = - 29$ $10 - 10y - 3y = -29$

$10 - 13 y = - 29$ $10 - 13y = -29$

$- 10 + 10 - 13 y = - 10 - 29$ $-color(red)(10) + 10 - 13y = -color(red)(10) - 29$

$0 - 13 y = - 39$ $0 - 13y = -39$

$- 13 y = - 39$ $-13y = -39$

$\frac{- 13 y}{- 13} = - \frac{39}{- 13}$ $(-13y)/color(red)(-13) = -39/color(red)(-13)$

$(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = 3$

$y = 3$

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

$x = 2 - 2y$ becomes:

$x = 2 - (2 xx 3)$

$x = 2 - 6$

$x = -4$

The solution is: $x = -4$ and $y = 3$ or $(-4, 3)$

How do solve the following linear system?: x+2y =2 , 5x - 3y = -29 x+2y=2,5x−3y=−29 x+2y =2 , 5x - 3y = -29 ?