How would I solve 3x-8y=5, and 4x-2y=11 to find points to plot on graph?

Question

How would I solve 3x-8y=5, and 4x-2y=11 to find points to plot on graph?

Answer 1

3x-8y=5(First you subtract 3x from 5 and you get -8y=5-3x. Then divide each side by -8 and you get Y=-5/8-3x. Enter that equation into a graphing calculator and thats how you graph it)

4x-2y=11(First subtract -4x from 11 and you get -2y=11-4x. Then divide each side by -2 and your final answer is Y=-11/2+2x. And enter that information into the calculator)

*Hope that helps*

Answer 2

4x-2y=11

3x-8y=5

Make either the x's the same or the y's the same (I'm going for ys)

Both y's need to be -8y so the first equation needs to be multiplied by 4 (multiply each part by 4)

which is 16x-8y=44

(broken down:

4x x 4 = 16x

-2y x 4 = -8y

11 x 4 = 44)

Now you need to take away the other equation

16x -8y = 44

3x -8y = 5

___________

13x = 39

(broken down:

16x - 3x = 13x

-8y- -8y = -8y + 8y = 0

44 - 5 =39)

13x = 39 therefore x = 3

YOU HAVE YOUR X CO-ORDINATE!

Now substitute x=3 into any of the equations, e.g. 3x-8y=5

9 - 8y = 5

+8y] 9 = 5 + 8y

-5] 4 = 8y

/8] 0.5=y

YOU HAVE YOUR Y CO-ORDINATE!

x = 3

y = 0.5

Plot that on your graph and thats where your two lines intersect

Answer 3

x = 3

y = 1/2

Answer 4

1. 3x-8y=5

2. 4x-2y=11 --> 16x-8y=44

Subtract 2 from 1

--> -13x=-39    (3x-16x)  (-8y-(-8y)) (5-44)

--> x = 3

Plug x into 1. or 2.

4(3)-2y=11 --> 12-2y=11 --> 2y=1 --> y=0.5

(x,y)=(3,0.5)

Answer 5

Rearrange each equation to the form y = mx + c

3x - 8y = 5 ==> 8y = 3x - 5 ==> y = (3/8)x - 5/8

4x - 2y = 11 ==> 2y = 4x - 11 ==> y = 2x - 11/2

Now plot a y-axis (vertical axis) with a x-axis (horizontal axis) with a scale.

Put random numbers in x to solve for y and plot it each point.

Example:

With equation y = 2x - 11/2 above, you can plot points like this:

When x=1 y=2(1)-11/2= -7/2 ==> ( 1 , -7/2 ) [ this a point ]

Keep on substituting values for x, any numbers you desire which can be plotted on your graph ( within the number limits your page can hold ) and solve to get y.

This way you'll find the solution to the problem graphically by finding the point of intersection of both lines, that would be your answer.

If you want to confirm algebraically ( more accurate since drawing includes errors ) then equate the equations for y or x as subject of formula, or you can use substitution/elimination methods.

Hope this helps.

Answer 6

to get the line of a equation first substitute x with any real number(an integer better in most cases) and solve the equation to get y.  The "substituted value of x" and "the corresponding value of y" are the coordinates. Do this to get at least three coordinates for a equation and join the points to get the line.

If you do this for second equation too, the two lines may

1) intersect then the point of intersection is the solution

2) coincide then there are infinite solutions ie all common points

3) be parallel then there are no solutions