Question

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??

Answer 1

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 :)

Answer 2

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.