X+y=25
Learn
well, its graph is a line.
Was there some question you wanted to ask?
The equation given is X + y = 25. This is a linear equation in two variables, X and y. To solve for either variable, we need another equation involving the same variables.
If you have a second equation, you can use the method of substitution or elimination to solve for X and y.
For example, let's say we have the equation 2x - y = 3 as the second equation. Now we can solve the system of equations.
Method 1: Substitution method
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for X: X = 25 - y.
Step 2: Substitute the expression for the variable into the other equation.
Substitute X = 25 - y into the second equation: 2(25 - y) - y = 3.
Step 3: Solve the resulting equation for the remaining variable.
Simplify the equation: 50 - 2y - y = 3.
Combine like terms: 50 - 3y = 3.
Subtract 50 from both sides: -3y = 3 - 50 = -47.
Divide both sides by -3: y = -47 / -3 = 47 / 3.
Step 4: Substitute the value of y back into one of the original equations to find the value of the other variable.
Using the first equation: X + y = 25.
Substitute y = 47 / 3: X + 47 / 3 = 25.
Multiply both sides by 3 to clear the fraction: 3X + 47 = 75.
Subtract 47 from both sides: 3X = 75 - 47 = 28.
Divide both sides by 3: X = 28 / 3.
So the solution to the system of equations is X = 28 / 3 and y = 47 / 3.
Method 2: Elimination method
Step 1: Multiply both sides of one or both equations by constants so that the coefficients of one variable will be the same or the negatives of each other.
In our case, we can multiply the first equation by -2 so that the coefficients of X become the negative of each other.
Step 2: Add or subtract the equations to eliminate one variable.
Subtracting the modified first equation from the second equation: (2x - y) - (-2x - 2y) = 3 - (-50).
Simplifying the equation: 2x - y + 2x + 2y = 3 + 50.
Combining like terms: 4x + 3y = 53.
Step 3: Solve the resulting equation for one variable.
In our case, let's solve for X: 4x = 53 - 3y.
Step 4: Substitute the value of the solved variable back into one of the original equations to find the value of the other variable.
Using the first equation: X + y = 25.
Substitute 4x = 53 - 3y: (53 - 3y) + y = 25.
Simplify the equation: 53 - 2y = 25.
Subtract 53 from both sides: -2y = 25 - 53 = -28.
Divide both sides by -2: y = -28 / -2 = 28 / 2 = 14.
Then substitute y = 14 back into X + y = 25: X + 14 = 25.
Subtract 14 from both sides: X = 25 - 14 = 11.
So the solution to the system of equations is X = 11 and y = 14.