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how would i solve step by step -3x+4y=8

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2 Answers

Hopefully you know how to isolate a variable. But if not lets isolate the y-variable together.
 
-3x + 4y = 8  Add 3x to both sides. *You can also chose to subtract 4y from both sides and still get the same result, but I'll leave that as an exercise for you.
 
4y = 3x +8    Now divide both sides by 4.  *Often students forget to put + 8 because the positive sign isn't there.
 
4y/4 = 3x/4 + 8/4  Simplify. *Divide the 3 and 8 each by 4 because they are separated by a plus(or minus) sign. Its a different story when there's multiplication or division. If you need help understanding that just let me know.
 
y = 3x/4 + 2  Final equation. * "Why isolate for y?" I can answer that too but for the mean time just do it.,
 
You only need two points to plot a graph for a linear equation ( a line). *"There are other types of equations?" you might ask? Yes but don't worry about them right now.
 
It's always a great choice to pick zero as the first number you use for x.
 
y = 3(0)/4 + 2 
y=2   You just found the y-intercept! It's where the graph of the line crosses the y (vertical) axis.
 
You could pick any other number for the second x-value but look closer at the final equation. it has a fraction. so how can we use this to our advantage? we have to try and use a number for x that makes the fraction turn into in integer( a non-fraction or a non-decimal). You could use a 4 because it will turn out like this:
y = 3(4)/4 + 2  The 4's will cancel and 
y= 3 + 2 
y = 5
 
Now all you have to do is use the two points. (0,2) and (4,5). This is the format for a point (x,y) *Some students have trouble with this, but if you need help just let me know.
 
So lets plot the points on a graph.
 
 
 
 
 
Now draw a line through the points ( a ruler helps) to see the line.
 
 
 
That's it. I hope this helps. Post to this thread if you want me to clarify anything else.
Have a great day!

Comments

You can really just plug start plugging in numbers for either x or y and solve for the other variable, like
-3(10) +4y = 8.  ---> -30 +4y = 8  ---> 4y = 38 ---> y = 9.5.  Therefore (10, 9.5) is a point you can graph. 
 
I wouldn't start with 10 though, I would start with 0 and then choose 4 and 8. (since 1,2,3,5,6,7 give you decimals)  also use -4 and -8.  That will give you 5 non decimal points.  I would also plug these numbers into x not y, really just out of habit.