Two systems of equations are shown below:
System A
6x + y = 2
−x − y = −3
System B
2x − 3y = −10
−x − y = −3
Which of the following statements is correct about the two systems of equations?
The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.
They will have the same solution because the first equations of both the systems have the same graph.
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.
Is it a??
by the way, now that we know, we go back and see why
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
GRAPH THEM ALL !!!
I tend to put them in the slope intercept form
y = m x + b
to graph them
System A
first
6x + y = 2
or y = - 6 x + 2
second
−x − y = −3
or y = -1 x + 3
now I can easily graph them
where do they cross?
-6x+2 = -1 x + 3
5 x =-1
x = -1/5
so intersection is
x = -1/5 and y = 3 1/5 = 16/5
(-1/5 , 16/5)
for the other one system B
2x − 3y = −10
is y = (2/3) x + 10/3
and
−x − y = −3
is y = -x + 3
so
-x+3 = (2/3) x + 10/3
or
-3 x + 9 = 2 x + 10
-5x=1
x = -1/5
then y = 16/5
so
(-1/5 , 16/5)
remarkable :)
No, the correct answer is:
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
No, the correct answer is not option a.
To determine the correct statement, we need to analyze the two systems of equations given.
For System A:
Equation 1: 6x + y = 2
Equation 2: -x - y = -3
For System B:
Equation 1: 2x - 3y = -10
Equation 2: -x - y = -3
Now let's evaluate the options:
Option a states that the value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A. However, this is not correct because the coefficient of x in the first equation of System B is actually 2, which is not 4 less than the coefficient of x in the first equation of System A (which is 6).
Option b states that the two systems will have the same solution because the first equations of both systems have the same graph. However, having the same graph does not guarantee having the same solution. The second equations in the systems are different, so this statement is not true.
Option c states that they will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A. Let's check if this is true:
System A, Equation 1 + (4 * Equation 2):
6x + y + (4 * -x - y)
= 6x + y - 4x - 4y
= 2x - 3y
As we can see, this does not result in the first equation of System B (2x - 3y = -10). So, this statement is also not correct.
Option d states that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding -4 to the first equation of System A and the second equations are identical. To check this, let's add -4 to the first equation of System A and compare it to the first equation of System B:
System A, Equation 1 + (-4):
6x + y - 4
= 6x + y - 4
= 2x - 3y - 4
As we can see, this does not result in the first equation of System B (2x - 3y = -10). Additionally, the second equations are not identical since the coefficients are different. So, this statement is also not correct.
Therefore, the correct answer is none of the above options.