## anonymous 5 years ago need a refresher solve the equations by graphing 3x+y=15 4x+5y=9

1. anonymous

To solve by graphing means graph each equation and see where they intersect.

2. anonymous

Do you know how to graph these?

3. anonymous

multiply first by 4 and second by 3 and subtract to eliminate x

4. anonymous

or multiply first by 5 and subtract from 2 to eliminate y

5. anonymous

ahhhhh......we r graphing.....damn

6. anonymous

give two values to x and y in the first equation to draw the line for first equation

7. anonymous

same with the second one.

8. anonymous

and check where it intersects !!

9. anonymous

so lets say (4,3) for the first equation

10. anonymous

The easiest way to graph a line is to find the intercepts by plugging in 0 for x, and solve for y, then plug in 0 for y and solve for x. That will give you two points $$(0,y_0)$$ and $$(x_0,0)$$. Then you just draw the line that connects them and that is the graph of the equation.

11. anonymous

3x+y=15 if x=0 then y=15

12. anonymous

Refer to the attached plot, $\text{Plot}\left[\left\{15-3x,\frac{9}{5}-\frac{4 x}{5}\right\},\{x,-1,8\}\right]$ The plot program requires that the two equations be solved for y. It then computes all of the points displayed. For each value of x between -1 and 8 it then computes the corresponding value for y. This plot program was running under an Apple 64 bit OS and the results are instantaneous. The fact is that a line is relatively simple to plot for a human because two points determine a line. If you know where the line crosses the x axis and where it crosses the y axis, then all you have to do is mark the two points on graph paper and draw a line through them with a ruler. The math lingo for these points is the x intercept and y intercept respectively. The process has been described fairly well by polpak's second posting. The expressions in the plot statement are the result of solving for y. If y is zero, in the first expression, then the corresponding x has to be 5 ie: (5,0) If you refer to the plot you will see the blue line crossing the x axis at (5,0). The blue line appears to cross the y axis at 15 or through the point (0,15). That is easy to confirm because when x is zero, 15 - 3x = 15. For the red line, the y intercept is easy to compute because when x = 0, 9/5 - 4/5 times x = 9/5 = 1.8 The solution to the problem is the point coordinates where they cross each other. In this case by eye ball, x=6 for sure and y is close to -3.