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

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asked 2021-02-14

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

Answers (1)

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.

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