How do you find an ordered pair for 4y + 1 = -3x and 5x + 6y = -3?

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Answer 1 · 2017-02-12T14:31:43

See the entire solution process below:

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

$4y + 1 = -3x$

$4y + 1 - color(red)(1) = -3x - color(red)(1)$

$4y + 0 = -3x - 1$

$4y = -3x - 1$

$(4y)/color(red)(4) = (-3x - 1)/color(red)(4)$

$(color(red)(cancel(color(Black)(4)))y)/cancel(color(red)(4)) = (-3x - 1)/4$

$y = (-3x - 1)/4$

Step 2) Substitute $(-3x - 1)/4$ for $y$ in the second equation and solve for $x$ :

$5x + 6y = -3$ becomes:

$5x + 6((-3x - 1)/4) = -3$

$5x - (18x)/4 - 6/4 = -3$

$color(red)(4)(5x - (18x)/4 - 6/4) = color(red)(4) xx -3$

$(color(red)(4) xx 5x) - (color(red)(4) xx (18x)/4) - (color(red)(4) xx 6/4) = -12$

$20x - (cancel(color(red)(4)) xx (18x)/color(red)(cancel(color(black)(4)))) - (cancel(color(red)(4)) xx 6/color(red)(cancel(color(black)(4)))) = -12$

$20x - 18x - 6 = -12$

$2x - 6 = -12$

$2x - 6 + color(red)(6) = -12 + color(red)(6)$

$2x - 0 = -6$

$2x = -6$

$(2x)/color(red)(2) = -6/color(red)(2)$

$(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -3$

$x = -3$

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

$y = (-3x - 1)/4$ becomes:

$y = ((-3 xx -3) - 1)/4$

$y = (9 - 1)/4$

$y = 8/4$

$y = 2$

The solution is: $x = -3$ and $y = 2$ or $(-3, 2)$