1. ## Algebra Help

I just don't understand these last 3 problems. -.-
Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

1. How many solutions are there to the following system of equations?
2x + 5y = -11
10x + 25y = -55

a. 0
b. 1
c. 2
d. infinitely many (I think this is the answer?)

2. How many solutions are there to the following system of equations?
5x + 3y = 7
2x - y = 2

a. 0
b. 1
c. 2
d. infinitely many.

3. Solve the following system of equations by linear combination:
2d + e = 8
d - e = 4

a. solution is (5,-2)
b. solution is (4,0)
c. no solution
d. infinite number of solutions.

2. Originally Posted by LamiaCat
I just don't understand these last 3 problems. -.-
Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

1. How many solutions are there to the following system of equations?
2x + 5y = -11
10x + 25y = -55

a. 0
b. 1
c. 2
d. infinitely many (I think this is the answer?) Yes - multiply eq1 by 5

2. How many solutions are there to the following system of equations?
5x + 3y = 7
2x - y = 2

a. 0
b. 1 Solve the second for y and substitute into the first
c. 2
d. infinitely many.

3. Solve the following system of equations by linear combination:
2d + e = 8
d - e = 4

a. solution is (5,-2)
b. solution is (4,0) Add the two equations together
c. no solution
d. infinite number of solutions.
See above

3. Originally Posted by LamiaCat
I just don't understand these last 3 problems. -.-
Can anyone help me? Please? Steps to solving would be appreciated so I can figure these out in the future!

1. How many solutions are there to the following system of equations?
2x + 5y = -11
10x + 25y = -55

a. 0
b. 1
c. 2
d. infinitely many (I think this is the answer?)
Hello LamiaCat,

Notice that the second equation is a multiple of the first. Each term is multiplied by 5. This means they represent the same line and have an infinite number of solutions. We call the system consistent and dependent.

Originally Posted by LamiaCat
2. How many solutions are there to the following system of equations?
5x + 3y = 7
2x - y = 2

a. 0
b. 1
c. 2
d. infinitely many.
Notice that the slopes of the graphs of these equations are not the same. So they are not parallel, nor are they the same line. That only leaves one possibility. They intersect in one point. We call the system consistent and independent.

Originally Posted by LamiaCat
3. Solve the following system of equations by linear combination:
2d + e = 8
d - e = 4

a. solution is (5,-2)
b. solution is (4,0)
c. no solution
d. infinite number of solutions.
Add the two equations together to eliminate e.

3d = 12
d = 4

Substitute back into either equation to find e = 0.