Question

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

Answer 1

Solution to a system of equation is values of variables true for all equations of that system.The x-value of solution to the given system is 2

How to find the solution to the given system of equation?

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

What is the equation of a line passing through two given points in 2 dimensional plane?

Suppose the given points are $(x_1, y_1)$ and $(x_2, y_2)$ , the n the equation of the straight line joining both two points is given by

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

The first equation is $2x + 4y = 0$

Since the second equation of line contains points given, let we consider two points,

$(x_1, y_1) = (-1,8)\\(x_2, y_2) = (3, -4)$

Then, the equation of line is found as:

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y - 8) = \dfrac{-4-8}{3-(-1)}(x - (-1))\\\\y = -3(x + 1) + 8\\\\3x + y = 5$

Thus, the system of equations is

$2x + 4y = 0\\3x + y = 5$

From second equation, getting y in terms of x(since its easy as y has 1 as coefficient), we get:

$3x + y = 5\\y = 5 - 3x$

Putting this value of y in first equation, we get:

$2x + 4y = 0\\\\2x + 4(5-3x) = 0\\20 = 10x\\x= 2$

Putting this value of x in expression  for y, we get:

$y = 5 - 3x = 5 - 6 = -1$

Thus, the solution to the system of equations obtained is (x,y) = (2,-1)

Thus, The x-value of solution to the given system is 2

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