Solve the following pair of linear equations :
x+y=5 2x−3y=4
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Step-by-Step Solution
Step 1: Multiply the first equation
To eliminate one of the variables, we can multiply the first equation by 3. This will make the coefficient of y in the first equation equal in magnitude and opposite in sign to the coefficient of y in the second equation.
Step 2: Add the modified equations
Now, add the modified first equation to the second equation. The y terms will cancel out, allowing us to solve for x.
Step 3: Solve for x
Divide both sides of the equation by 5 to find the value of x.
Step 4: Substitute x into the first equation
Substitute the value of x back into the original first equation (x+y=5) to solve for y.
Step 5: Solve for y
Subtract 519 from 5 to find the value of y. Convert 5 to a fraction with a denominator of 5 to perform the subtraction.