Question

Solve the system by graphing the lines. Express your answer as an ordered pair.0.7x+0.8y=310 0.1x+0.4y=330 The solution is

Answer 1

The ordered pairs are (-700, 1000)

Graphical Method

This is used to solve simultaneous equations to find the ordered pairs

To solve this problem, we are asked to solve the simultaneous equation by graphing method.

Attached below is a copy of the graph

However, we can also use substitution method or elimination method to check our answer.

The point of intersection is where we have the solution to the problem which are called ordered pair and in this graph, it's at point (-700, 1000).

Elimination Method

This is used to solve a simultaneous equation by eliminating one of the variables

`\begin{gathered} 0.7x+0.8y=310\ldots\text{equation(i)} \\ 0.1x+0.4y=330\ldots equation(ii)_{} \end{gathered}`

From euqtaion (ii), multpily through by 2. This is to help us eliminate y in both equations.

`\begin{gathered} 2(0.1x+0.4y=330) \\ 0.2x+0.8y=660\ldots\text{equation (}ii) \end{gathered}`

Now, let's bring both equations together.

`\begin{gathered} 0.7x+0.8y=310\ldots\text{equation(}i) \\ 0.2x+0.8y=660\ldots\text{equation(}ii) \end{gathered}`

Let subtract equation (ii) from equation (i).

The equation will become

`\begin{gathered} 0.7x+0.8y=310 \\ - \\ 0.2x+0.8y=660 \\ = \\ 0.5x+0=-350 \end{gathered}`

Now we have an equation

`\begin{gathered} 0.5x=-350 \\ (0.5x)/(0.5)=-(350)/(0.5) \\ x=-700 \end{gathered}`

Let's substitute the value of x in either eqaution (I) or equation (II).

Using equation (i)

`\begin{gathered} 0.7x+0.8y=310 \\ 0.7(-700)+0.8y=310 \\ -490+0.8y=310 \\ 0.8y=310-(-490) \\ 0.8y=310+490 \\ 0.8y=800 \\ (0.8y)/(0.8)=(800)/(0.8) \\ y=1000 \end{gathered}`

From the calculations above, the ordered pairs is (-700, 1000) for which statisfy the value of x and y respectively in the equations