We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
346
1
avatar+209 

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

Best Answer 

 #1
avatar+2339 
+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.
\(x=7\)  
   


 

 Jan 4, 2018
 #1
avatar+2339 
+2
Best Answer

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

19 Online Users

avatar
avatar