Question

Find the solution to the system { -1/3x+y=1, 2x+5y=-28

Answer 1

To solve the system of equations, we first isolate y in the first equation and then substitute this expression into the second equation to find x. After determining x, we find y, leading us to the solution (x, y) = (-6.27, -3.09).

Step-by-step explanation:

We are asked to find the solution to the system of equations:

• -1/3x + y = 1
• 2x + 5y = -28

First, let's isolate y in the first equation:

1. Multiply through by -3 to clear the fraction: x - 3y = -3.
2. Now, express y in terms of x: y = (1/3)x - 1.

Next, we'll substitute the expression for y into the second equation:

1. Replace y in 2x + 5y = -28 with the expression from step 2: 2x + 5((1/3)x - 1) = -28.
2. Simplify and solve for x: 2x + (5/3)x - 5 = -28, which leads to (11/3)x = -23, so x = -23 * 3/11, x = -69/11, x = -6.27 (approximately).
3. Finally, find y using the expression from step 2: y = (1/3)(-6.27) - 1, y = -2.09 - 1, y = -3.09 (approximately).

Thus, the solution to the system of equations is approximately (x, y) = (-6.27, -3.09).