Question

Given the system of equations: 5x + 2y = 3 4x − 8y = 12 Solve for (x, y) using elimination.

Answer 1

To solve the system of equations using elimination, multiply the equations to make the coefficients of a variable equal, then subtract the equations to eliminate that variable. Solve for the remaining variable and substitute its value to find the other variable. The solution to the given system of equations is (x, y) = (1, -1).

Step-by-step explanation:

To solve the given system of equations using elimination, we'll eliminate one variable by adding or subtracting the equations. Let's eliminate the variable 'x'.

1. Multiply the first equation by 4 and the second equation by 5 to make the coefficients of 'x' equal: 20x + 8y = 12 and 20x - 40y = 60.
2. Subtract the second equation from the first equation to eliminate 'x': (20x + 8y) - (20x - 40y) = 12 - 60.
3. Simplify the equation: 48y = -48.
4. Divide both sides by 48 to solve for 'y': y = -1.
5. Substitute the value of 'y' into either original equation to solve for 'x': 5x + 2(-1) = 3.
6. Simplify the equation: 5x - 2 = 3.
7. Add 2 to both sides: 5x = 5.
8. Divide both sides by 5 to solve for 'x': x = 1.

The solution to the system of equations is (x, y) = (1, -1).