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)
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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.