Question

Solve system of linear equations with -4x y=-21 and -2x 4y=14

Answer 1

To solve the system of linear equations -4x + y = -21 and -2x + 4y = 14, we can use the elimination method, which results in the solution x = 9/4 and y = -4⅗3.

Step-by-step explanation:

The question asks to solve a system of linear equations which consists of the two equations -4x + y = -21 and -2x + 4y = 14. To solve this system, we can use either substitution or elimination methods. Let's use the elimination method for this exercise.

1. Multiply the first equation by 2 to make the coefficient of x in both equations the same. This gives us -8x + 2y = -42.
2. Add the new equation from step one to the second original equation to eliminate the x variable: (-8x + 2y) + (-2x + 4y) = -42 + 14.
3. Simplify and solve for y: 6y = -28; y = -28 / 6; y = -4⅗3.
4. Now substitute y = -4⅗3 back into either original equation to find x. Using the first equation: -4x - 4⅗3 = -21.
5. Solve for x: -4x = -21 + 4⅗3; -4x = -21 + 12; -4x = -9; x = -9 / -4; x = 9/4 or 2.25.

Therefore, the solution to the system of equations is x = 9/4 and y = -4⅗3.