Solve the System of Equations
{2x−y=103x+2y=1\begin{cases}
2x-y=10\
3x+2y=1\

\end{cases}
Solve the system of equations. Simplify your answers.
x = [Fill in the blank]

y = [Fill in the blank]

Question

Solve the System of Equations
{2x−y=103x+2y=1\begin{cases}
      2x-y=10\
     3x+2y=1\
      
    \end{cases}   
Solve the system of equations. Simplify your answers.
x = [Fill in the blank]

y = [Fill in the blank]

BlackTom AI · Accepted Answer

The problem asks us to solve a 2x2 linear system and fill in the values for x and y. 
First, I identify the two equations clearly: 2x − y = 10 and 3x + 2y = 1. 
From the first equation, I can express y in terms of x: y = 2x − 10. 
Next, I substitute this expression for y into the second equation to eliminate y: 3x + 2(2x − 10) = 1. 
This expands to 3x + 4x − 20 = 1, which simplifies to 7x − 20 = 1. 
Solving for x gives 7x = 21, so x = 3. 
With x known, I substitute back into y = 2x − 10: y = 2(3) − 10 = 6 − 10 = −4. 
Thus, the solution to the system is x = 3 and y = −4. 
Note: There were no answer choices provided to evaluate or compare against; the solution is unique for this linear system, so these are the correct fill-ins for the blanks. 
If you wanted to verify, plug the values back into both original equations: 2(3) − (−4) = 6 + 4 = 10, and 3(3) + 2(−4) = 9 − 8 = 1, which satisfy both equations.

MAT-265-OD24-02-7799 Prior Knowledge Check

Solve the System of Equations {2x−y=103x+2y=1\begin{cases} 2x-y=10\\ 3x+2y=1\\ \end{cases} Solve the system of equations. Simplify your answers. x = [Fill in the blank] y = [Fill in the blank]

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