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?
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. |
\(x=7\) | |
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. |
\(x=7\) | |