3x+2y=2
−2x+y=8
(1 point)
Responses
(4, -2)
(4, -2)
(-4, 2)
(-4, 2)
(-2, 4)
(-2, 4)
(14, -20)
(4, -2)
To solve this system of equations:
Step 1: Choose one of the equations and solve it for one variable in terms of the other variable.
Let's choose the second equation and solve it for y:
-2x + y = 8
y = 2x + 8
Step 2: Substitute the expression for y from step 1 into the other equation.
3x + 2(2x + 8) = 2
3x + 4x + 16 = 2
7x + 16 = 2
Step 3: Simplify and solve for x.
7x = 2 - 16
7x = -14
x = -14/7
x = -2
Step 4: Substitute the value of x into one of the original equations to solve for y.
3(-2) + 2y = 2
-6 + 2y = 2
2y = 2 + 6
2y = 8
y = 8/2
y = 4
So, the solution to the system of equations is (x, y) = (-2, 4).
To solve the given system of equations:
3x + 2y = 2 ...(Equation 1)
-2x + y = 8 ...(Equation 2)
There are a couple of methods to solve this system, such as substitution or elimination. Let's use the method of elimination:
1. Multiply Equation 2 by 2 to make the coefficients of 'y' in both equations the same:
-2x + y = 8
(multiply by 2)
-4x + 2y = 16 ...(Equation 3)
2. Now, subtract Equation 3 from Equation 1:
(3x + 2y) - (-4x + 2y) = 2 - 16
3x + 2y + 4x - 2y = -14
7x = -14
Divide both sides by 7:
x = -2
3. Substitute the value of 'x' back into either Equation 1 or Equation 2. Let's use Equation 1:
3x + 2y = 2
3(-2) + 2y = 2
-6 + 2y = 2
Add 6 to both sides:
2y = 8
Divide both sides by 2:
y = 4
So, the solution to the system of equations is (x, y) = (-2, 4).
Therefore, the correct response is (-2, 4).