What is the answer and steps for x plus y equals 1 2x-y equals -2 in the substitution method?

Answer 1

To solve the system of equations using the substitution method:

1. Solve one of the equations for a variable (e.g., x) in terms of the other variable (e.g., y). From the first equation, x = 1 - y.
2. Substitute the expression for x into the second equation. Replace x in the second equation with (1 - y), giving 2(1 - y) - y = -2.
3. Simplify and solve for y. Expanding and rearranging, we get 2 - 2y - y = -2. Combining like terms, -3y = -4, so y = 4/3.
4. Substitute the value of y back into the first equation to solve for x. x = 1 - (4/3) = 3/3 - 4/3 = -1/3. Therefore, the solution to the system of equations is x = -1/3 and y = 4/3.

Answer 2

x + y = 1

therefore x = 1 - y.

2x - y = -2

substituting x = 1 - y in this equation gives 2*(1 - y) - y = -2

That is, 2 - 2y - y = -2

or -3y = -4 => y = 4/3.

Then x = 1 - y => x = 1 - 4/3 = -1/3.

Therefore, the solution is (x, y) = (-1/3, 4/3).