Solving System of Equations All Ways

When solving a system of equations algebraically, which statement results in infinite solutions?

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

Use Substitution to solve the system:

x = 2y - 9

2x + 3y = 17

• (1,2)

• (1,5)

• (5,1)

• (2,1)

3x + y = 1
y = 4x + 1

• (0, -1)

• No Solution

• (0, 8)

• (0, 1)

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1.5)

Which of the following are correct ways to solve this system by elimination? There could be more than one correct answer. Choose ALL that work!!

• Multiply the first equation by 3 and multiply the second equation by 5.

• Multiply the first equation by -3 and multiply the second equation by 5.

• Multiply the first equation by -3 and multiply the second equation by -5.

• Multiply the first equation by 3 and multiply the second equation by -5.

Answer explanation

Which of the following are correct ways to solve this system by elimination? There could be more than one correct answer. Choose ALL that work!!

• Multiply the first equation by 4 and multiply the second equation by -7.

• Multiply the first equation by -4 and multiply the second equation by 7.

• Multiply the first equation by -9 and multiply the second equation by -8.

• Multiply the first equation by 9 and multiply the second equation by 8.

Answer explanation

What's the first step to eliminate the y's from this system of equations?

• Multiply the first equation by a number.

• Multiply the second equation by a number.

• It is NOT necessary to multiply either equation by a number.

• Multiply both equations by different numbers.

Answer explanation

We could multiply the first equation by -1 giving us -2y and 2y (so the y's would cancel out)

OR we could multiply the second equation by -1 giving us 2y and -2y (so the y's would cancel out)

What's the first step to eliminate the y's from this system of equations?

• Multiply the first equation by a number.

• Multiply the second equation by a number.

• It is NOT necessary to multiply either equation by a number.

• Multiply both equations by different numbers.

Answer explanation

If we add the equations as they are the y's will cancel out - there is no need to multiply either equation by any number.

What's the first step to eliminate the y's from this system of equations?

• Multiply the first equation by a number.

• Multiply the second equation by a number.

• It is NOT necessary to multiply either equation by a number.

• Multiply both equations by different numbers.

Answer explanation

If we multiply the first equation by 7, then we will have 7y in the first equation and -7y in the second equation. So that when we add the equations the y's will cancel out.