solving with elimination 7x-4y=13 2x-5y =-4
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To solve the system of equations using the elimination method, follow these steps:
Step 1: Choose a variable to eliminate.
In this case, we will eliminate the variable "x" by multiplying the first equation by the coefficient of "x" in the second equation, and the second equation by the coefficient of "x" in the first equation.
Step 2: Multiply the equations to create opposite coefficients.
Multiply the first equation by 2 and the second equation by 7:
Equation 1: 2(7x - 4y) = 2(13) => 14x - 8y = 26
Equation 2: 7(2x - 5y) = 7(-4) => 14x - 35y = -28
Step 3: Add or subtract the equations to eliminate the variable.
Subtract Equation 2 from Equation 1 to eliminate the variable "x":
(14x - 8y) - (14x - 35y) = 26 - (-28)
Simplify: -8y + 35y = 26 + 28
Combine like terms: 27y = 54
Step 4: Solve for the remaining variable.
Divide both sides of the equation by 27:
27y / 27 = 54 / 27
Simplify: y = 2
Step 5: Substitute the value of y back into one of the original equations.
Let's substitute y = 2 into the first equation:
7x - 4(2) = 13
Simplify: 7x - 8 = 13
Add 8 to both sides of the equation:
7x = 21
Divide both sides of the equation by 7:
x = 3
Step 6: Write the final solution as an ordered pair (x, y).
The solution to this system of equations is (x, y) = (3, 2).