How to find x and Y? Please include both methods thanks

Question

y=-2x+9

3x-4y=8

Answer 1

The 1st method that Min provided was the algebraic one.  I will show the second, which is the graphical one.

 

You two equation that represent straight lines.  These lines are drawn on the same coordinate system.  When these lines intersect, they will share a common point.  This point is known as the point of intersect and is the solution to the system of equations.

 

To graph these equations, you need to put them in  y=mx+b form , where m is slope and b is y-intercept.

 

The first equation is already in this form.  Slope is -2 and y-intercept is 9.

 

 

We do need to convert the second equation into this form.

 

-4y = -3x + 8

 

   y = (3/4)x - 2

 

 

The slope is 3/4 and y-intercept is -2.

 

 

Now that you have your equations written in this form, use the slope and y-intercept to graph each of these lines.

 

 

For the first equation:

 

Plot the point (0, 9).  This is your y-intercept and the first point on this line.

 

Then plot the second point using the slope.  From this first point, move 1 unit to the right, and 2 units down.   The second point is (1, 7).

 

Connect these points to get your straight line.  Extend the line so that it covers the entire coordinate system.

 

 

For the second equation:

 

First point is  (0, -2)

 

Move 4 units to the right and 3 unit up from the first point to get your second point.

 

Second point is  (4, 1)

 

 

Connect these points in a straight line.  The line should cover the entire the coordinate system.  Once you have your lines, look for the point of intersection.  That will be your solution.

Answer 2

Hi,

 

First, I substitute y = -2x + 9 into the second equation :

3x - 4(-2x + 9) = 8

becomes

3x + 8x - 36 = 8

11x = 44

x=4

then,

y = -2x+9 = -2*4 + 9 = 1

 

Hope it helps!