To solve the system of equations y = −x − 1 and y = 3x − 5, we can set the two equations equal to each other and solve for x:
−x − 1 = 3x − 5
Subtract 3x from both sides:
−4x − 1 = −5
Add 1 to both sides:
−4x = −4
Divide by −4:
x = 1
Now that we have x = 1, we can substitute this value back into either of the original equations to solve for y. Let's use y = 3x − 5:
y = 3(1) − 5
y = 3 - 5
y = -2
Therefore, the solution to the system is (1, -2). Let's check the other points given to verify if they are correct solutions:
1. (-1, 1):
y = -(-1) - 1
y = 1 - 1
y = 0
This point does not satisfy the second equation, so it is not a solution.
2. (0, -1):
y = -0 - 1
y = -1
This point satisfies both equations, so it is a valid solution.
3. (2, 1):
y = -2 - 1
y = -3
This point does not satisfy the first equation, so it is not a solution.
Therefore, the correct solutions to the system of equations are:
(1, -2) and (0, -1)
Solve the system: y = −x − 1 y = 3x − 5
(-1, 1)
(0, -1)
(1, -2)
(2, 1)
5 answers
x - y = -1
x - 3y =-13
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
x - 3y =-13
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
To check if the point (5, 6) is the solution to the linear system of equations x - y = -1 and x - 3y = -13:
1. Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true:
Equation 1: 5 - 6 = -1
-1 = -1 (True)
Equation 2: 5 - 3(6) = -13
5 - 18 = -13
-13 = -13 (True)
Both equations are true when substituting (5, 6) for x and y, so (5, 6) is a solution to the system of equations.
It is not necessary to follow the other methods to check the solution once it has been confirmed that (5, 6) satisfies both equations in the system.
1. Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true:
Equation 1: 5 - 6 = -1
-1 = -1 (True)
Equation 2: 5 - 3(6) = -13
5 - 18 = -13
-13 = -13 (True)
Both equations are true when substituting (5, 6) for x and y, so (5, 6) is a solution to the system of equations.
It is not necessary to follow the other methods to check the solution once it has been confirmed that (5, 6) satisfies both equations in the system.
bot you have to choose an answer
The correct way to check if the point (5, 6) is the solution to the linear system of equations x - y = -1 and x - 3y = -13 is to substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Therefore, the correct method to check the solution is: Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Therefore, the correct method to check the solution is: Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.