Solving Systems by Substitution Warmup 3

What does a "solution to a system of equations" mean?

• It's the point where both equations equal zero

• It's the point where graphs of both equations cross the y-axis

• It's the point that is true for both equations at the same time

• It's the point where graphs of both equations cross the x-axis

Answer explanation

A solution to a system of equations is a point that will work in all equations within the system.

When solving a system of equations algebraically, which statement results in no solution?

• 4 = 7

• -2 = 2

• -3 = 3

• all of the above

Answer explanation

You will be left with a contradiction (something false) when trying to solve a system of equations, if there is no solution.

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

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

Answer explanation

You will be left with an identity (something true) when trying to solve a system of equations, if there are infinitely many solutions.

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Solve the system of equations using substitution

x=-6y

2x+12y=0

• (-6, 1)

• (0, 0)

• (1, -6)

• No solution

• Infinite solutions

Solve the system of equations using substitution

y=-5x

x+3y=28

• (-6, 30)

• (-2, 10)

• (44, 39)

• No solution

• Infinite solutions