Question

A system of equations is created by using the line represented by 2x+4y= 0 and the line represented by the data in the table below. x -1 3 5 6 у 8 -1 3 5 -10 6 -13 What is the x-value of the solution to the system?

Answer 1

To find what we are looking for we first need to find the second equation.

To do this we need to use the equation of a line:

`y-y_1=m(x-x_1)`

where (x1,y1) is a point on the line and m is the slope. The slope of a line is given by:

`m=(y_2-y_1)/(x_2-x_1)`

Using the first two points on the table we get:

`\begin{gathered} m=(-4-8)/(3-(-1)) \\ =(-12)/(4) \\ =-3 \end{gathered}`

Now that we have the slope we plug it in the equation of a line with the values of any of the points in the table (we are going to use the first one). Then:

`\begin{gathered} y-8=-3(x-(-1)) \\ y-8=-3(x+1) \\ y-8=-3x-3 \\ 3x+y=5 \end{gathered}`

Now that we have the equation of the second line we conclude that we have the system of equations:

`\begin{gathered} 2x+4y=0 \\ 3x+y=5 \end{gathered}`

To find the x value of the solution we solve the second equation for y, then:

`y=5-3x`

now we plug this value into the first equation and solve for x:

`\begin{gathered} 2x+4(5-3x)=0 \\ 2x+20-12x=0 \\ -10x=-20 \\ x=(-20)/(-10) \\ x=2 \end{gathered}`

Therefore, the x value of the solution of the system is 2.