Mathematics: Asystem of equations is created by using the line represented by 2x+4y=0 and the line represented by the data in the table below. –1 8 3 –4 5 –10 6 –13 (not answer choices! ^) what is the x-value of the solution to the system?

Asystem of equations is created by using the line

brennarfa

14.03.2022

We have been given the first equation as 2x+4y=0

Now, we find the second equation from the given table. From the table, we have two points (-1,8),(3,-4)

The slope of the line is given by

$m=\frac{y_2-y_1}{x_2-x_1}\\
\\
m=\frac{-4-8}{3+1}\\
\\
m=\frac{-12}{4}\\
\\
m=-3$

Thus, the equation of the line is given by

$y-y_1=m(x-x_1)\\
y-8=-3(x+1)\\
y-8=-3x-3\\
y=-3x+5$

Therefore, we have the system of equations

$2x+4y=0...............(1)\\
y=-3x+5................(2)$

Substitute the value of y in equation 1, we get

$2x+4(-3x+5)=0\\
2x-12x+20=0\\
-10x=-20\\
\\
x=\frac{-20}{-10} \\
\\
x=2$

The x value is given by 2

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