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# MAFS.8.EE.3.8

Analyze and solve pairs of simultaneous linear equations.
1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
3. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Remarks/Examples

Examples of Opportunities for In-Depth Focus

When students work toward meeting this standard, they build on what they know about two-variable linear equations, and they enlarge the varieties of real-world and mathematical problems they can solve.

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: SHT , EE , MI , GRID item(s)

• Assessment Limits :
Numbers in items must be rational numbers. Coefficients of equations in standard form must be integers. Items written for MAFS.8.EE.3.8a must include the graph or the equations. Equations in items written for MAFS.8.EE.3.8a must be given in slope-intercept form.
• Calculator :

Yes

• Context :

Allowable

### SAMPLE TEST ITEMS (8)

• Test Item #: Sample Item 2
• Question:

Analyze the system of two equations shown.

y=3(x+4)

y=3(x-4)

How many solutions does the system of equations have?

• Difficulty: N/A
• Type: SHT: Selectable Hot Text

• Test Item #: Sample Item 4
• Question:

A graph of a system of two equations is shown.

What is the approximate solution of the system?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 5
• Question:

A system of two equations is shown.

y = 5x + 3

y = 3x - 1

A. Use the Add Arrow tool to graph the two lines.

B. Drag the palette image to show the solution of the system.

• Difficulty: N/A
• Type: GRID: Graphic Response Item Display

• Test Item #: Sample Item 6
• Question: Radha is trying to choose between two bike rental companies, Company A and Company B.

Company A charges a \$25 initial fee and an additional \$5 for each hour rented. Company B charges an initial \$18 fee and an additional \$6 for each hour rented.

The total cost to rent a bike from Company A can be represented by the equation y=5h+25, where h represents the number of hours rented and y represents the cost, in dollars.

The total cost to rent a bike from Company B can be represented by the equation y=6h+18, where h represents the number of hours rented and y represents the cost, in dollars.

For how many hours of rental is the amount charged by the two companies the same? What is the cost, in dollars, of renting the bike for this many hours?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 7
• Question: Enter values for ?? and ??, so that the system of equations shown has one solution.

y = 3x + 4

y = ax + b

• Difficulty: N/A
• Type: EE: Equation Editor