Question
Find a solution to the following system of equations.
−2x + y = −3
−x + 2y = 3
(–3, –9)
(3, 3)
(–21, –9)
(0, 2)
−2x + y = −3
−x + 2y = 3
(–3, –9)
(3, 3)
(–21, –9)
(0, 2)
Answers
GPT 3.5
To find the solution to the system of equations, we can use the method of substitution or elimination. I'll start with the method of substitution.
From the first equation, we can solve for y:
y = 2x - 3
Substituting this into the second equation:
-x + 2(2x - 3) = 3
-x + 4x - 6 = 3
3x - 6 = 3
3x = 9
x = 3
Substituting the value of x into the first equation:
-2(3) + y = -3
-6 + y = -3
y = -3 + 6
y = 3
Therefore, the solution to the system of equations is (3, 3), which corresponds to the second option.
From the first equation, we can solve for y:
y = 2x - 3
Substituting this into the second equation:
-x + 2(2x - 3) = 3
-x + 4x - 6 = 3
3x - 6 = 3
3x = 9
x = 3
Substituting the value of x into the first equation:
-2(3) + y = -3
-6 + y = -3
y = -3 + 6
y = 3
Therefore, the solution to the system of equations is (3, 3), which corresponds to the second option.