Determine Systems of Linear Equations

What are systems of linear equations?

• a set of two or more linear equations in the same variables
• a polynomial with three terms
• set of two or more linear inequalities in the same variables

How can you tell if a point is a solution to a system?

• It makes the first equation true when checking the solution.

• The (x,y) coordinates satisfy both equations when checking the solution.

• It makes logical sense.

• It makes neither equation negative.

Determine if (4 , 1) is a solution for the system of equations.

y = -x + 5

y = 2x - 7

• Yes

• No

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Solve the following system of equations by graphing:

• (4, -4)

• (-4, 4)

• no solutions

• (0, 0)

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Solve the following system of equations using substitution:

• Infinite solutions

• (2, -2)

• (1, 0)

• (3, -4)

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Solve the following system of equations using the elimination method:

• (-2, 1)

• no solutions

• (-2, 0)

• (-1, -3)