Solve Graphically the following simultaneous linear equations
5x+7y=13
7x+6y=3
but i want to knw how can i make its 4 order pairs
come on, guy. For the first equation, pick any two values. Make them easy ones.
y=-1, x=4
x=-3, y=4
So, plot (4,-1) and (-3,4) and draw the line.
Do the same for the other one.
5x+7y=13
7x+6y=3
4x - y - 10 =0
3x - 5y - 19 =0
To solve the simultaneous linear equations graphically, we will plot the graphs of the two equations on a coordinate plane, and find the point of intersection, which represents the solution.
Let's start with the first equation, 5x + 7y = 13.
To plot this equation graphically, we need to rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
7y = -5x + 13
y = (-5/7)x + 13/7
Now, to plot the first equation, we'll choose some arbitrary x-values and calculate the corresponding y-values.
For example, let's choose x = 0:
y = (-5/7)(0) + 13/7
y = 13/7
Thus, we have the first coordinate point (0, 13/7).
Similarly, let's choose another x-value, say x = 2:
y = (-5/7)(2) + 13/7
y = -10/7 + 13/7
y = 3/7
The second coordinate point is (2, 3/7).
By repeating this process, we can get more points. Alternatively, we can use the slope to get more points by moving up and down or left and right depending on the slope.
Now, let's plot these points on the graph.
Next, let's move on to the second equation, 7x + 6y = 3.
Similarly, we rearrange the equation to slope-intercept form:
6y = -7x + 3
y = (-7/6)x + 1/2
Again, we choose some x-values and calculate the corresponding y-values to plot the equation.
For example, let's choose x = 0:
y = (-7/6)(0) + 1/2
y = 1/2
Thus, we have the first coordinate point (0, 1/2).
Similarly, let's choose x = 2:
y = (-7/6)(2) + 1/2
y = -14/6 + 1/2
y = -13/6 + 1/2
y = -7/6
The second coordinate point is (2, -7/6).
Plot these points on the graph.
Once both equations are plotted on the same coordinate plane, we can visually observe the point of intersection. This point represents the solution to the simultaneous equations.
In this case, the point of intersection appears to be approximately (2, -7/6).
Hence, the solution to the simultaneous linear equations 5x + 7y = 13 and 7x + 6y = 3 is x = 2 and y = -7/6.
c'mon. Can you plot points?
Plot two points for each equation. Connect the pairs into lines. See where the lines intersect.