Question

what is the gradient of 20x=2y+15

Answer 1

Answer:

Often it is necessary to look at several functions of the same independent variable. Consider the prior example where x, the number of items produced and sold, was the independent variable in three functions, the cost function, the revenue function, and the profit function.

In general there may be:

n equations

v variables

Solving systems of equations

There are four methods for solving systems of linear equations:

a. graphical solution

b. algebraic solution

c. elimination method

d. substitution method

Graphical solution

Example 1

given are the two following linear equations:

f(x) = y = 1 + .5x

f(x) = y = 11 - 2x

Graph the first equation by finding two data points. By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

If x = 0, then f(0) = 1 + .5(0) = 1

If y = 0, then f(x) = 0 = 1 + .5x

-.5x = 1

x = -2

The resulting data points are (0,1) and (-2,0)

Graph the second equation by finding two data points. By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

If x = 0, then f(0) = 11 - 2(0) = 11

If y = 0, then f(x) = 0 = 11 - 2x

2x = 11

x = 5.5

The resulting data points are (0,11) and (5.5,0)

At the point of intersection of the two equations x and y have the same values. From the graph these values can be read as x = 4 and y = 3.