If a = -12/5, then 5x + 2y = 6 and 3x - ay = 4 are parallel.
1 answer:
<span><span><span><span>5x </span>+<span>2y </span></span></span>=<span>6
</span></span>Add -2y to both sides
<span><span>5x</span>=<span><span>−<span>2y</span></span>+6
</span></span><span><span><span></span></span></span>Divide both sides by 5
<span>x=<span><span><span><span><span>−2/</span>5</span></span>y </span>+<span><span> <span>6/5</span></span>
</span></span></span><span><span><span>that into the second equation:
</span></span></span>
<span><span><span>3<span>(<span><span><span><span><span>−2/</span>5</span></span>y</span>+<span><span><span>6/5</span></span></span></span>)</span></span>+<span><span><span>12/5</span></span>y </span></span>=4
simplify
</span><span><span><span><span><span>6/5</span></span>y</span>+<span><span><span>18/5</span></span> </span></span>=4
</span>Add (-18)/5 to both sides
<span><span><span><span>6/5</span></span>y</span>=<span><span>2/<span>5
divide both sides by 6/5
y = 1/3
substitute 1/3 for y in x = -2/5y +6/5 to solve for x
x = -2/5(1/3) +6/5
x = 16/15
so x = 16/15 and y = 1/3
now replace both x and Y in each of the original equations to check the answers:
5(16/15) +2(1/3) = 5 1/3 + 2/3 = 6 true
3(16/15) - -12/5(1/3) = 4 true
so they are parallel
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