What is the solution to the system of equations that contains –3x + y = 3 and 2x – y = –1?
A.
no solution
B.
(–1, 3)
C.
infinite number of solutions
D.
(–2, –3)
Add the two equations.
-x = 2
-4 - y = -1
y = ?
To find the solution to the system of equations, we can use the method of elimination.
First, let's add the two equations together:
(-3x + y) + (2x - y) = 3 + (-1)
Simplifying the equation, we have:
-x = 2
Next, let's solve for x by multiplying both sides of the equation by -1:
x = -2
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
-3(-2) + y = 3
Simplifying the equation, we have:
6 + y = 3
Then, solve for y by subtracting 6 from both sides:
y = 3 - 6
y = -3
Therefore, the solution to the system of equations is (x, y) = (-2, -3).
So the answer is D. (–2, –3).
To solve the system of equations, we can use the method of substitution.
First, let's solve one equation for one variable and substitute it into the other equation.
From equation 1, -3x + y = 3, we can rearrange it to solve for y:
y = 3 + 3x
Next, we substitute this expression for y into equation 2, 2x - y = -1:
2x - (3 + 3x) = -1
Simplifying this equation, we get:
2x - 3 - 3x = -1
-x - 3 = -1
-x = 2
x = -2
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.
Using equation 1, -3x + y = 3:
-3(-2) + y = 3
6 + y = 3
y = -3
Therefore, the solution to the system of equations is (x, y) = (-2, -3).
So the answer is D. (–2, –3).