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Algebra elimination sequence. Help?

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The equation is 4x+8y=20 and -4x+2y=-30 where I am told to find X and Y using elimination. Anyone have any ideas?

Jan 4, 2018

#1
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Let's line the equation up side by side.

$$\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30$$

Take note of the bit highlighted in red. Do you notice how the coefficients are opposite of each other? This is important! If I were to add these equations together as is, then the x would cancel out.

$$\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\\ \overline{\quad\quad\quad\quad\quad\quad\quad\quad}\\ \hspace{2mm}0x+10y=-10$$

We can solve for y pretty easily by dividing by -10. Of course, 0x simplifies to 0, so the x has disappeared.

$$10y=-10\\ \hspace{5mm}y=-1$$

We can now plug in this y value into the the original equation and solve for x. I'll plug it into the first one.

 $$4x+8y=20$$ We already know that y=-1, so let's substitute that in for y and solve for the remaining unknown. $$4x+8(-1)=20$$ 8*-1 can be simplified. $$4x-8=20$$ Add 8 to both sides. $$4x=28$$ Finally, divide by 4 to isolate x completely. $$x=7$$

Jan 4, 2018

#1
+2

Let's line the equation up side by side.

$$\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30$$

Take note of the bit highlighted in red. Do you notice how the coefficients are opposite of each other? This is important! If I were to add these equations together as is, then the x would cancel out.

$$\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\\ \overline{\quad\quad\quad\quad\quad\quad\quad\quad}\\ \hspace{2mm}0x+10y=-10$$

We can solve for y pretty easily by dividing by -10. Of course, 0x simplifies to 0, so the x has disappeared.

$$10y=-10\\ \hspace{5mm}y=-1$$

We can now plug in this y value into the the original equation and solve for x. I'll plug it into the first one.

 $$4x+8y=20$$ We already know that y=-1, so let's substitute that in for y and solve for the remaining unknown. $$4x+8(-1)=20$$ 8*-1 can be simplified. $$4x-8=20$$ Add 8 to both sides. $$4x=28$$ Finally, divide by 4 to isolate x completely. $$x=7$$

TheXSquaredFactor Jan 4, 2018