SOLUTION: 3x +7y=3 and 12x +28y =16 Here is what they want. Use either elimination or substitution to fine the solutions (if any). Graph the two lines, and list the x-intercepts. y-inte

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 3x +7y=3 and 12x +28y =16 Here is what they want. Use either elimination or substitution to fine the solutions (if any). Graph the two lines, and list the x-intercepts. y-inte      Log On


   

Question 476008: 3x +7y=3 and 12x +28y =16
Here is what they want.
Use either elimination or substitution to fine the solutions (if any).
Graph the two lines, and list the x-intercepts. y-intercepts, and points of intersection.
In order to earn credit for the slope and intercepts, you must explicitly write each of these sentences, filling in the blanks with the correct values for that problem.
A. For equation______
1. The x-intercept is_____
2. The y-intercept is _____
3.The slope is_______
B. For equation______
1. The x-intercept is_____
2. The y-intercept is _____
3.The slope is_______
Please help me to do this and understand how its done.
Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x+%2B7y=3 and
12x+%2B28y+=16
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x%2B7y=3

12x%2B28y=16





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x%2B7y=3 Start with the given equation



7y=3-3x Subtract 3+x from both sides



7y=-3x%2B3 Rearrange the equation



y=%28-3x%2B3%29%2F%287%29 Divide both sides by 7



y=%28-3%2F7%29x%2B%283%29%2F%287%29 Break up the fraction



y=%28-3%2F7%29x%2B3%2F7 Reduce



Now lets graph y=%28-3%2F7%29x%2B3%2F7 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F7%29x%2B3%2F7%29+ Graph of y=%28-3%2F7%29x%2B3%2F7




So let's solve for y on the second equation


12x%2B28y=16 Start with the given equation



28y=16-12x Subtract 12+x from both sides



28y=-12x%2B16 Rearrange the equation



y=%28-12x%2B16%29%2F%2828%29 Divide both sides by 28



y=%28-12%2F28%29x%2B%2816%29%2F%2828%29 Break up the fraction



y=%28-3%2F7%29x%2B4%2F7 Reduce





Now lets add the graph of y=%28-3%2F7%29x%2B4%2F7 to our first plot to get:


Graph of y=%28-3%2F7%29x%2B3%2F7(red) and y=%28-3%2F7%29x%2B4%2F7(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.


write both equations in slope-intercept form:
3x+%2B7y=3.....->....7y=-3x%2B3.....->....y=-%283%2F7%29x%2B3%2F7
12x+%2B28y+=16.....->....28y+=-12x%2B16.....->....y+=-%2812%2F28%29x%2B16%2F28.....->....y+=-%283%2F7%29x%2B4%2F7

A. For equation__3x+%2B7y=3____
1. The x-intercept is__at (1)___
2. The y-intercept is __at 3%2F7___
3.The slope is___-%283%2F7%29____
B. For equation______
1. The x-intercept is_at %284%2F7%29%2F%283%2F7%29=4%2F3____
2. The y-intercept is __at 4%2F7___
3.The slope is_____-%283%2F7%29__