Algebra 1 Systems of Equations

Solve the system by elimination.
  5x + 8y = -12
3x + 5y = -7

• (1, -10)

• No solution

• (-4, 1)

• (1, 10)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Which of the answers below are methods to

solve a system of linear equations? Select an

that apply.

• Graphing

• Parallel

• Substitution

• Elimination

• Distributive

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is a solution to a system of equations?

• The x-value of a coordinate point.

• The y-value of a coordinate point.

• The coordinate point where the equations intersect when graphed.

• Any coordinate point on one line when graphed

Answer explanation

The solution to a system is a point that lies on all lines when graphed

This is also called an intersection point

The solution in this example is (1, 1) because that is where the lines intersect.

Tags

CCSS.8.EE.C.8B

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

The solution to a system is at the intersection point of the lines

These two lines intersect at one point, so there is one solution!

Tags

CCSS.8.EE.C.8B

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

Same slope

Same y-intercept

Same line = infinitely many solutions

Lines go on forever, these lines intersect at every point, for infinity!

***YOU MUST SOLVE FOR Y IN ORDER TO DETERMINE THE SLOPE AND Y-INTERCEPT***

Tags

CCSS.8.EE.C.8B

Which graph represents the solution to this system of equations?

• 
• 
• 

Answer explanation

You must identify the slope and y-intercept of each line

Line 1:

slope=2

y-intercept=-3

Line 2:

slope: -1

y-intercept: 3

The line with a y-int. of 3 should have a positive slope. Only option A shows this.

Tags

CCSS.8.EE.C.8B

Solve the system

(a)  

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the system

(a)  

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

At a candy store, Anna bought 5 pieces of bubble gum and 3 pieces of fudge for $3.25. Tia bought 2 pieces of bubble gum and 3 pieces of fudge for $4.05. Which system of equations could be used to find b, the cost of one piece of bubble gum, and f, the cost of one piece of fudge?

• 
• 
• 
• 

Tags

CCSS.8.EE.C.8C

Which of the following graphs best represents the solution of the system of inequalities?

• 
• 
• 
• 

Answer explanation

Tags

CCSS.HSA.REI.D.12