Question

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3x + 2y = 2 -2x+y = 8 (1 point) O (14, -20) O (-4, 2) O (4, -2) O (-2, 4)

Answer 1

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution to find the solution:

We have the first equation: 3x + 2y = 2.

We can solve this equation for x:
3x = 2 - 2y
x = (2 - 2y)/3

Now, substitute this expression for x into the second equation:
-2(2 - 2y)/3 + y = 8

Multiply through by 3 to eliminate the fraction:
-4(2 - 2y) + 3y = 24
-8 + 8y + 3y = 24
11y = 32
y = 32/11

Now substitute this value of y into the first equation to solve for x:
3x + 2(32/11) = 2
3x + 64/11 = 2
3x = 2 - 64/11
3x = 22/11 - 64/11
3x = -42/11
x = -14/11

Thus, the solution to the system of equations is (x, y) = (-14/11, 32/11).

Therefore, the correct answer is O (-4, 2).