Given:
Total cost of cupcakes and cookies = $20
Let x be the numbers of cupcakes and let y represents the number of cookies.
We can form a system of two linear equations from the question given.
5x + 1.25y = 20
y = 4x
We can now proceed to graph the equations.
To graph, we need to get the points. Find the x and y-intercept of the first equation.
To find the x -intercept, put y = 0 and solve for x
5x + 1.25(0) = 20
5x = 20
x=4
The x-intercept is (4, 0)
To find the y-intercept, put x= 0 and solve for y.
5(0) + 1.25y = 20
1.25y = 20
y= 16
The y-intercept is (0, 16)
The two points for the first equations are (4, 0) and (0,16)
Similarly, for the second equation find the x and y- intercept to get the points.
y = 4x
y - intercept = (0, 0)
X - intercept = (0, 0)
Hence, the point for the second equation is (0,0)
Below is the graph of the system of equations.
The solution to this system of equation is where the two lines intersect.
Hence, x = 2 and y= 8
Therefore, the number of cupcakes bought is 2 and the number of cookies bought is 8.