You can use any of the available methods for solving system of linear equations like method of elimination or method of substitution etc.
There are no solutions to the given system of equations.
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.
Using the above method to solve the given system of equations
The given system of equations is
[tex]2x - 6y = 5\\x - 3y = -12[/tex]
Using second equation to get x in terms of y
[tex]x - 3y - 12\\x = 3y - 12[/tex]
Substituting this expression for x in place of x in first equation,
[tex]2x - 6y = 5\\2( 3y - 12) - 6y = 5\\6y - 24 - 6y = 5\\-24 = 5[/tex]
The last statement we got is incorrect.
That conclusion above shows that the given system of equation has no solution.
We could've detected it from the fact that
[tex]2x - 6y = 5\\\text{dividing both sides by 2}\\x - 3y = 2.5[/tex]
Converting both equations to slope intercept form, we get:
[tex]x - 3y = 0.5\\\\y = \dfrac{1}{3}x - \dfrac{1}{6}[/tex]
and
[tex]x - 3y = -12\\\\y = \dfrac{1}{3}x + 4[/tex]
We see that both lines have same slope but different y intercept, which tells that both lines are parallel but not coincident, thus, not intersecting and thus, no common point(common points are solutions).
The graph of this system of linear equation is given below where lines represented by both linear equations are plotted.
Thus,
There are no solutions to the given system of equations.
Learn more about system of linear equations here:
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