MATH SOLVE

4 months ago

Q:
# 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.–1 83 –45 –106 –13(not answer choices!^)What is the x-value of the solution to the system?

Accepted Solution

A:

We have been given the first equation as [tex]2x+4y=0[/tex]Now, we find the second equation from the given table. From the table, we have two points [tex](-1,8),(3,-4)[/tex]The slope of the line is given by[tex]m=\frac{y_2-y_1}{x_2-x_1}\\
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m=\frac{-4-8}{3+1}\\
\\
m=\frac{-12}{4}\\
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m=-3[/tex]Thus, the equation of the line is given by[tex]y-y_1=m(x-x_1)\\
y-8=-3(x+1)\\
y-8=-3x-3\\
y=-3x+5[/tex]Therefore, we have the system of equations[tex]2x+4y=0...............(1)\\
y=-3x+5................(2)[/tex]Substitute the value of y in equation 1, we get[tex]2x+4(-3x+5)=0\\
2x-12x+20=0\\
-10x=-20\\
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x=\frac{-20}{-10} \\
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x=2[/tex]The x value is given by 2