Solve each system graphically.
#6.
4x - y = 9
x - 3y = 16
I need to find at least one pair of points that fit. I tried using the elimination method and got (5 and 6/7, -22), which did not even work for the first equation.
I also tried graphing it but it was too hard to tell.
Can anyone help me with solving this?
Thanks so much! :-)
you can try substitution
y=4x-9
x-3(4x-9) = 16
x - 12x + 27 = 16
-11x=-11
x=1
4-y=9
y=-5
(1,-5)
x+5y=7
-2x-7y=-5
4x+y=14 x + y = 1
x+y=-2
2×_3y=_24×+6y=18
To solve the system graphically, you need to plot the equations on a coordinate grid and find the points of intersection. Here's how you can do it:
1. Start by rearranging each equation in terms of y:
Equation 1: 4x - y = 9 --> y = 4x - 9
Equation 2: x - 3y = 16 --> y = (x - 16) / 3
2. Choose a range of x-values to plot the lines. It's usually helpful to pick values that are easy to work with. Let's choose x = -5, 0, and 5.
3. Plug each x-value into the equations to find the corresponding y-values:
For Equation 1:
When x = -5, y = 4(-5) - 9 = -29
When x = 0, y = 4(0) - 9 = -9
When x = 5, y = 4(5) - 9 = 11
For Equation 2:
When x = -5, y = (-5 - 16) / 3 = -7
When x = 0, y = (0 - 16) / 3 = -16/3
When x = 5, y = (5 - 16) / 3 = -11/3
4. Plot the corresponding points on the coordinate grid. Label each point with its coordinates.
5. Draw a straight line connecting the points for each equation. You may notice that the lines intersect at a certain point.
6. Locate the point of intersection on the graph to find the solution. In this case, it seems that the lines do not intersect at a single point. Therefore, the system is inconsistent, meaning it has no solution.
It's always good to double-check your work by re-plugging the coordinates into both original equations to verify the solution. In this case, since there is no point of intersection, the system is inconsistent, and there is no solution that satisfies both equations.
Didn't your question ask for a graphical solution?
so you have to find at least 2 ordered pairs for each equation and then draw them
for the first:
4x - y = 9 ---> y = 4x - 9
x y
1 -5
3 3
for the second:
x - 3y = 16 ---> x = 3y + 16
x y
4 -4
-2 6
graph both lines, they should intersect at (1,-5), the answer chopsticks gave you.