Ans 4/10 8. Solve the following system of linear equations: $3x + y = 10$ $x - y = 2$ Ans $x = 3$ , $y = 1$ (system of linear equations, elimination method, substitution method, simultaneous equations)

Answer: $x = 3$ , $y = 1$

Step-by-step solution

Step 1: Identify the equations

We are given two linear equations. Let's label them as Equation (1) and Equation (2) for easy reference. Our goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.

Step 2: Eliminate one variable

Notice that the coefficients of $y$ in both equations are $+1$ and $-1$ . If we add Equation (1) and Equation (2), the $y$ terms will cancel out, allowing us to solve for $x$ . This method is called the elimination method.

Step 3: Solve for x

Now that we have a simple equation with only $x$ , we can solve for $x$ by dividing both sides by 4.

Step 4: Substitute x to find y

Now that we have the value of $x$ , we can substitute $x=3$ into either of the original equations to find $y$ . Let's use Equation (1): $3x + y = 10$ .

Step 5: Verify the solution

To ensure our solution is correct, we substitute $x=3$ and $y=1$ into both original equations. Since both equations are satisfied, our solution is correct.

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Ans 4/10 8. Solve the following system of linear equations: 3x+y=103x + y = 103x+y=10 x−y=2x - y = 2x−y=2 Ans x=3x = 3x=3, y=1y = 1y=1 (system of linear equations, elimination method, substitution method, simultaneous equations)