What is the solution of the system? y = −3x 3x + 2y = 6 (1 point) Responses (2, 6) (2, 6) (−1, 3) (−1, 3) (−2, 6) (−2, 6) (1.5, −4.5
To solve the system, we can substitute the value of y from the first equation into the second equation:
3x + 2(-3x) = 6
3x - 6x = 6
-3x = 6
x = -2
Now we can substitute this value back into the first equation to find the value of y:
y = -3(-2)
y = 6
Therefore, the solution to the system is (-2, 6).
To solve the system of equations, we can use the substitution method.
First, let's rearrange the first equation to solve for x:
y = -3x
Divide both sides by -3 to isolate x:
x = -y/3
Next, substitute this expression for x in the second equation:
3x + 2y = 6
Replace x with -y/3:
3(-y/3) + 2y = 6
Simplify:
-y + 2y = 6
Combine like terms:
y = 6
Now that we have y = 6, let's substitute this value back into the first equation to solve for x:
x = -y/3
x = -(6)/3
Simplify:
x = -2
The solution to the system of equations is (x, y) = (-2, 6).
To find the solution of the system, we need to solve the given equations simultaneously. Let's go step by step to find the answer.
1. Given equations are:
y = -3x ...(Equation 1)
3x + 2y = 6 ...(Equation 2)
2. We will use the method of substitution to solve the system. From Equation 1, we know that y = -3x. We can substitute this value of y into Equation 2.
Substitute y = -3x in Equation 2.
3x + 2(-3x) = 6
3. Simplify the equation by distributing the 2 to -3x.
3x - 6x = 6
4. Combine like terms.
-3x = 6
5. Divide both sides of the equation by -3 to solve for x.
x = -2
6. Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y.
y = -3(-2)
y = 6
7. Therefore, the solution to the system of equations is x = -2 and y = 6.
Hence, the correct answer is (−2, 6).