Question

Use the substitution method to solve the system x=y-4;+8y=2 (1 point) (-3 1/3, 2/3) Infinite solutions no solution (2/3, -3 1/3)

Answer 1

To use the substitution method, we start by solving one of the equations for one variable and substituting it into the other equation.

Considering the first equation: x = y - 4, we can solve it for x by adding 4 to both sides: x + 4 = y.

Now we substitute this expression for x in the second equation: 8(y) = 2.

Now we simplify the equation: 8y = 2.

Solving for y, we divide both sides by 8: y = 2/8.

Thus, the value of y is 2/8, which simplifies to 1/4.

Now we substitute this value for y in the expression we found earlier: x = y - 4. So, x = (1/4) - 4.

Simplifying the expression, we have x = -15/4.

Therefore, the solution to the system of equations is (x, y) = (-15/4, 1/4), which can also be written as (-3 3/4, 1/4).

The closest option to this solution is (-3 1/3, 2/3), so the correct answer is (2/3, -3 1/3).