The solution of given system of equations is [tex]\boxed{(10,-1)}[/tex].
Further explanation
The system of equations is given as follows:
[tex]\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}[/tex]
The equations are the form of linear equation in two variables.
The general form of linear equation in two variables is [tex]ax+by+c=0[/tex] where [tex]a,b,c[/tex]are real numbers.
Here, the system of equations is as follows:
[tex]x+3y=7[/tex] .....(1)
[tex]2x-4y=24[/tex] ......(2)
Now, we can rewrite the equation (1) as follows:
[tex]x=7-3y[/tex]
Substitute the value of [tex]x=7-3y[/tex] in equation (2) as follows:
[tex]2(7-3y)-4y=24[/tex]
Solve the above expression to find the value of [tex]y[/tex].
[tex]\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]-1[/tex].
Now, Substitute the value of [tex]y=-1[/tex] in equation (1) to get the value of [tex]x[/tex].
[tex]\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]10[/tex].
The solution of given system of equations is [tex](10,-1)[/tex].
Option (a)
In option (a) it is given that the solution is [tex](2,-6)[/tex].
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (a) is incorrect.
Option (b)
In option (b) it is given that the solution is [tex](10,-1)[/tex].
As per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (b) is correct.
Option (c)
In option (c) it is given that the solution is [tex](-2,8)[/tex].
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].
Therefore, option (c) is incorrect.
Option (d)
In option (d) it is given that there are infinte solution.
But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex] which is a unique solution.
Therefore, option (d) is incorrect.
Learn more
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equations in two variables
Keywords: Linear equations in one variable, linear equations in two variables, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open interval.
