Question

Find the solution (x,y)to the system of equations.\begin{cases}3x + y = 28\\-x+3y=4\end{cases}Multiply the coordinates x*y

Equations

Find the solution (x,y)to the system of equations.
$$\begin{cases}3x + y = 28\\-x+3y=4\end{cases}$$
Multiply the coordinates $$x \cdot y$$

2021-02-16

Step 1
Given:
The system of equations are,
$$3x+y=28...(1)$$
$$-x+3y=4...(2)$$
The objective is to find the solution of the coordinates (x,y) and multiply them.
Step 2
The system of equations can be solved by multiplying the equation (2) by 3.
$$3x+y=28$$
$$-3x+9y=12$$
On solving the above two equations for y,
$$10y=40$$
$$\displaystyle{y}={\frac{{{40}}}{{{10}}}}$$
$$y=4$$
Step 3
Substitute the value of y in (2) to find the value of x.
$$-x+3y=4$$
$$-x+3(4)=4$$
$$-x+12=4$$
$$-x=4-12$$
$$x=-4+12$$
$$x=8$$
Thus, the solution of coordinates is (8,4)
Multiplication of x and y is,
$$x \cdot y=8 \cdot 4$$
$$x \cdot y=32$$
Hence, multiplication of the coordinates is 32.