Algebra 1: Systems of Equations Test Review

Which of the answers below are methods to

solve a system of linear equations? Select an

that apply.

• Graphing

• Parallel

• Substitution

• Elimination

• Distributive

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.

State the clear solution to the system graphed.

Answer explanation

The solution is where the lines in a system INTERSECT!

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

Parallel lines do not interest

The solution to a system is the intersection point

No intersection point = no solution

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

We are told this is a system, that means there are at least two lines graphed.

It looks like one line because both lines are the same

Same exact line = infinelty many solutions

(this is because they intersect at every point, and the lines go on forever!)

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!

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

Different slope

Different y-intercept

One solution

(Remember a solution to a system is where the lines intersect on the graph)

How many solutions does the systems have?

• No solution

• One solution

• Infinitely many solutions

Answer explanation

Same slope

Different y-intercept

Parallel Lines = No solution

Parallel lines do not intersect, therefore there is no solution

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***

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.