Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x - 2y = -16
Answers)
A) graphing
B) substitution
C) elimination
D) distributive
C) elimination
What is the solution of the system?
7x + 5y = 19
-7x - 2y = -16
Answers)
A) (2, 1)
B) (1, 2)
C) (7, 5)
D) (-7, -2)
To solve the system, we can use the elimination method. By adding the two equations, the x-terms cancel out:
(7x + 5y) + (-7x - 2y) = 19 + (-16)
3y = 3
y = 1
Substituting this value of y in either equation, we can solve for x:
7x + 5(1) = 19
7x + 5 = 19
7x = 14
x = 2
Therefore, the solution to the system is (2, 1).
The correct answer is A) (2, 1).
Which method would be the simplest way to solve the system?
y = 1/2x
2x + 3y = 28
Answers)
A) graphing
B) substitution
C) elimination
D) distributive
B) substitution
What is the solution of the system?
y = -3x
3x + 2y = 6
Answers)
A) (2, 6)
B) (-1, 3)
C) (-2, 6)
D) (1.5, -4.5)
To solve the system, we can use the substitution method. Since y is already isolated in the first equation, we can substitute the expression for y into the second equation:
3x + 2(-3x) = 6
3x - 6x = 6
-3x = 6
x = -2
Substituting this value of x back into the first equation, we can solve for y:
y = -3(-2)
y = 6
Therefore, the solution to the system is (-2, 6).
The correct answer is C) (-2, 6).
How many solutions does this system have?
-3x + 6y = 10
-3x + 6y = -4
Answers)
A) none
B) one
C) infinite
D) two
From the given system of equations:
-3x + 6y = 10
-3x + 6y = -4
We can notice that the coefficients of x and y are the same in both equations, and the right sides of the equations are different. This means that the equations represent two parallel lines.
Since the lines are parallel and never intersect, there are no common solutions. Therefore, the system has:
The correct answer is A) none.
In which quadrant does the solution of the system fall?
y = x - 1
y = -3x - 5
Answers)
A) I
B) II
C) III
D) IV
To determine in which quadrant the solution of the system falls, we can find the intersection point between the two lines.
Setting the two given equations equal to each other:
x - 1 = -3x - 5
Simplifying the equation:
4x = -4
x = -1
Substituting this value of x into either equation, we can solve for y:
y = -1 - 1
y = -2
Therefore, the solution of the system is (-1, -2). This point falls in Quadrant III.
The correct answer is C) III.