How do you solve -2x -8y = 4 and x+ 16y = 22?

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Answer 1 · 2015-09-06T23:29:40

${(x = -10), (y = 2) :}$

Your system of equations looks like this

${(-2x - 8y = 4), (x + 16y = 22) :}$

Multiply the second equation by $2$ to get

${(-2x - 8y = 4), (x + 16y = 22 | * (2)) :}$

${(-2x - 8y = 4), (2x + 32y = 44) :}$

Add these two equations by taking the left-hand sides and the right-hand sides separately

$-color(red)(cancel(color(black)(2x))) - 8y + color(red)(cancel(color(black)(2x))) + 32y = 4 + 44$

$24y = 48 implies y = 48/24 = 2$

Take this value of $y$ into one of the original equations and solve for $x$

$x + 16 * (2) = 22$

$x + 32 = 22 implies x = -10$

The solution set for this system will be

${(x = -10), (y = 2) :}$