SOVING SYSTEM OR EQUATIONS BY ELIMINATION
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To solve a system of equations by elimination, follow these steps:
1. Write down the given system of equations.
Let's say we have the following system:
Equation 1: 2x + 3y = 10
Equation 2: 4x - 2y = 6
2. Choose one variable to eliminate.
Look for a variable in either equation that, when multiplied by a constant, can cancel out the coefficient of the same variable in the other equation. In this case, we can eliminate the variable "y" by multiplying Equation 1 by 2.
Multiply Equation 1 by 2:
2 * (2x + 3y) = 2 * 10
This becomes: 4x + 6y = 20
3. Align the equations vertically.
Write down the new equation with the original Equation 2 below it:
4x + 6y = 20
4x - 2y = 6
4. Add or subtract the equations.
Add or subtract the equations vertically in a way that eliminates one of the variables. In this case, if we subtract Equation 2 from Equation 1, the "x" terms will cancel out:
(4x + 6y) - (4x - 2y) = 20 - 6
Simplify: 4x - 4x + 6y + 2y = 14
This becomes: 8y = 14
5. Solve for the remaining variable.
Divide both sides of the equation by the coefficient of the remaining variable to isolate the variable. In this case, divide both sides by 8:
(8y) / 8 = 14 / 8
This simplifies to: y = 1.75
6. Substitute the value of the remaining variable back into one of the original equations to solve for the other variable.
Let's substitute the value of y into Equation 1:
2x + 3(1.75) = 10
Simplify: 2x + 5.25 = 10
Subtract 5.25 from both sides: 2x = 10 - 5.25
Simplify: 2x = 4.75
Divide both sides by 2: x = 2.375
7. Check the solution.
Substitute the values of x and y back into both original equations to verify that they satisfy each equation.
Equation 1: 2(2.375) + 3(1.75) = 10
Simplify: 4.75 + 5.25 = 10
This is true.
Equation 2: 4(2.375) - 2(1.75) = 6
Simplify: 9.5 - 3.5 = 6
This is also true.
Therefore, the solution to the system of equations is x = 2.375 and y = 1.75.