3x+2y=2
−2x+y=8
A. (14, -20)
B. (4, -2)
C. (-4, 2)
D. (-2, 4)
To solve this system of equations, we can use the method of substitution.
From the second equation, we can solve for y:
-2x + y = 8
=> y = 2x + 8
Now we can substitute this value of y into the first equation:
3x + 2(2x + 8) = 2
3x + 4x + 16 = 2
7x + 16 = 2
7x = -14
x = -2
Substituting this value of x back into the second equation, we can find y:
-2(-2) + y = 8
4 + y = 8
y = 4
Thus, the solution to the system of equations is (x, y) = (-2, 4).
Therefore, the correct answer is D. (-2, 4).
To solve the system of equations:
Step 1: We can start by solving the second equation for y in terms of x.
-2x + y = 8
y = 2x + 8
Step 2: Substitute the value of y in the first equation.
3x + 2(2x + 8) = 2
3x + 4x + 16 = 2
7x + 16 = 2
Step 3: Solve for x.
7x = 2 - 16
7x = -14
x = -14/7
x = -2
Step 4: Substitute the value of x into the equation derived in Step 1 to find y.
y = 2(-2) + 8
y = -4 + 8
y = 4
Step 5: The solution to the system of equations is (x, y) = (-2, 4).
Therefore, the correct answer is D. (-2, 4).
To solve the system of equations, you can use the method of substitution or the method of elimination. Let's use the method of substitution to find the solution.
First, let's solve the second equation for y:
-2x + y = 8
Add 2x to both sides:
y = 2x + 8
Now substitute this expression for y in the first equation:
3x + 2(2x + 8) = 2
Simplify and solve for x:
3x + 4x + 16 = 2
7x + 16 = 2
7x = -14
x = -2
Now substitute this value of x back into one of the original equations to find the value of y:
-2(-2) + y = 8
4 + y = 8
y = 8 - 4
y = 4
The solution to the system of equations is (x, y) = (-2, 4).
Checking the given options, we can see that the correct answer is D. (-2, 4).