1.
y=3x-7
y=-x+1
A. One Solution***
B. Infinitely Many
C. No Solution
2.
x+3y=12
x=y-8
A. One Solution
B. Infinitely Many***
C. No Solution
3.
x+y=5
x+y=-2
A. One Solution
B. Infinitely Many***
C. No Solution
@Ms. Sue can you help?
#1,#2: the lines have different slopes, so they will intersect in one point
#3 The lines are parallel, so they will not intersect at all.
You should try graphing the lines to see what happens. If you don't have any graph paper, there are lots of online graphing sites.
Thank you
I guessed it was
1. One Solution
2. One Solution
3. No Solution
To solve the system of equations and determine the number of solutions, we can use the method of substitution or elimination.
1. For the system of equations y = 3x - 7 and y = -x + 1:
We can solve this system by using the method of substitution. We substitute the expression for y from the second equation into the first equation:
3x - 7 = -x + 1.
Solving for x:
3x + x = 1 + 7,
4x = 8,
x = 2.
To find the value of y, we can substitute the value of x back into either one of the original equations. Let's use the second equation:
y = -x + 1,
y = -2 + 1,
y = -1.
Since we found unique values for both x and y, the system of equations has one solution. Therefore, the answer is A. One Solution.
2. For the system of equations x + 3y = 12 and x = y - 8:
We can solve this system using the method of substitution. We substitute the expression for x from the second equation into the first equation:
(y - 8) + 3y = 12.
Simplifying and solving for y:
4y - 8 = 12,
4y = 20,
y = 5.
To find the value of x, we substitute the value of y back into either one of the original equations. Let's use the second equation:
x = y - 8,
x = 5 - 8,
x = -3.
Since we found unique values for both x and y, the system of equations has one solution. Therefore, the answer is A. One Solution.
3. For the system of equations x + y = 5 and x + y = -2:
We can solve this system using the method of elimination. By subtracting the two equations, we eliminate the variable y:
(x + y) - (x + y) = 5 - (-2),
0 = 5 + 2,
0 = 7.
The equation 0 = 7 is not true, which means there is no solution that satisfies both equations simultaneously. Therefore, the answer is C. No Solution.