Question

Solve the system

Answer 1

Attached a solution and showed work.

Answer 2

The solution of given system of equations is $\boxed{(10,-1)}$.

Further explanation

The system of equations is given  as follows:

$\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}$

The equations are the form of linear equation in two variables.

The general form of linear equation in two variables is $ax+by+c=0$ where $a,b,c$are real numbers.

Here, the system of equations is as follows:

$x+3y=7$      .....(1)

$2x-4y=24$  ......(2)

Now, we can rewrite the equation (1) as follows:

$x=7-3y$  

Substitute the value of $x=7-3y$ in equation (2) as follows:

$2(7-3y)-4y=24$  

Solve the above expression to find the value of $y$.

$\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}$  

Therefore, the value of $y$ is $-1$.

Now, Substitute the value of $y=-1$ in equation (1) to get the value of $x$.

$\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}$  

Therefore, the value of $x$ is $10$.

The solution of given system of equations is $(10,-1)$.

Option (a)

In option (a) it is given that the solution is $(2,-6)$.

But as per the calculation solution of the given system of equations is $(10,-1)$.

Therefore, option (a) is incorrect.

Option (b)

In option (b) it is given that the solution is $(10,-1)$.

As per the calculation solution of the given system of equations is $(10,-1)$.

Therefore, option (b) is correct.

Option (c)

In option (c) it is given that the solution is $(-2,8)$.

But as per the calculation solution of the given system of equations is $(10,-1)$.

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 $(10,-1)$ which is a unique solution.

Therefore, option (d) is incorrect.

Learn more

1. Problem on the equation of the circle brainly.com/question/1952668

2. Problem on the center and radius of an equation brainly.com/question/9510228

3. Problem on the general form of the equation of the circle brainly.com/question/1506955

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.