Free · Printable · TEKS A.5C · Linear Functions, Equations, Inequalities
TEKS A.5C Worksheets — Algebra I Solve systems of two linear equations with
200+ Texas-aligned practice questions on this exact Algebra I standard. Print at home or practice online with a built-in AI tutor. No sign-up, no paywall.
What TEKS A.5C says: Solve systems of two linear equations with two variables for mathematical and real-world problems.
This page has 200+ practice questions tagged specifically to TEKS A.5C. Below: a sample of 8 with answers and explanations so you can preview the worksheet before printing. Every question goes through an AI quality gate (gpt-4o for content review, Claude Sonnet 4.5 for math verification) before publishing.
Cognitive demand: high. Typical question shape: System of equations; substitution or elimination.
Alejandra is helping her father with a cattle drive near Austin, Texas. They noticed that the number of cattle in their herd is related to the number of fences they have. The total cost for buying cattle is represented by the equation 3x + 200 = 5y, where x is the number of cattle and y is the number of fences. After buying some additional cattle, they spent a total of 800 dollars, which can be represented by the equation 3x + 200 = 800. How many cattle do they have in total?
- 200 ✓
- 180
- 200/3
- 100
Why: To find the number of cattle, we first solve the equation 3x + 200 = 800. Subtracting 200 from both sides gives us 3x = 600. Dividing by 3 gives us x = 200. Therefore, Alejandra and her father have 200 cattle in total.
Sky is organizing a charity soccer game in McAllen, Texas, and is selling tickets. Adult tickets cost $10 each, and student tickets cost $6 each. If Sky sold a total of 100 tickets and collected $800 in ticket sales, how many adult tickets did he sell?
- 40
- 50 ✓
- 60
- 70
Why: Let x represent the number of adult tickets sold and y represent the number of student tickets sold. We have two equations based on the problem: x + y = 100 (the total number of tickets) and 10x + 6y = 800 (the total amount collected). We can solve this system of equations using substitution or elimination. From the first equation, we can express y as y = 100 - x. Substituting this into the second equation gives us: 10x + 6(100 - x) = 800. Simplifying this: 10x + 600 - 6x = 800, or 4x + 600 = 800. Subtracting 600 from both sides gives us 4x = 200. Dividing by 4, we find x = 50. Therefore, Sky sold 50 adult tickets.
Daniel is planning a picnic in the Piney Woods of Texas and wants to buy sandwiches and drinks. The cost of sandwiches is $4 each, and the cost of drinks is $1.50 each. If Daniel has a budget of $30 and wants to buy the same number of sandwiches and drinks, which equation can be used to find the number of each item he can buy?
- 4x + 1.5x = 30 ✓
- 4x + 1.5 = 30
- 4 + 1.5x = 30
- 4x + 1.5x = 30x
Why: To find the number of sandwiches and drinks Daniel can buy, let x represent the number of each item. The total cost of sandwiches and drinks is given by the equation: cost of sandwiches + cost of drinks = budget. This translates to 4x (for sandwiches) + 1.5x (for drinks) = 30. Thus, the correct equation is 4x + 1.5x = 30.
Camila is selling cookies for a school fundraiser in San Antonio. She sells chocolate chip cookies for $2 each and oatmeal raisin cookies for $3 each. If she sells a total of 50 cookies and collects $120, which system of equations can be used to represent the number of chocolate chip cookies, x, and oatmeal raisin cookies, y, that Camila sold?
- x + y = 50 and 2x + 3y = 120 ✓
- x + 3y = 120 and 2x + y = 50
- 2x + 3y = 50 and x + y = 120
- 3x + 2y = 120 and x + y = 50
Why: To solve this problem, we first recognize that Camila sold a total of 50 cookies, which gives us the equation x + y = 50. Next, since she collected a total of $120 from selling those cookies, we can represent the total revenue from both types of cookies as 2x + 3y = 120. Therefore, the correct system of equations that models this scenario is x + y = 50 and 2x + 3y = 120.
Justice is helping his family run a fruit stand in the DFW Metroplex. They sell oranges for $2 each and apples for $3 each. One day, they sold a total of 50 fruits, earning $120. What is the number of oranges sold?
- 20
- 30 ✓
- 40
- 10
Why: Let the number of oranges sold be x and the number of apples sold be y. We can set up the following system of equations based on the problem: 1) x + y = 50 (the total number of fruits) and 2) 2x + 3y = 120 (the total earnings). To solve, we can express y in terms of x from the first equation: y = 50 - x. Substituting this into the second equation gives us 2x + 3(50 - x) = 120. Simplifying this, we have 2x + 150 - 3x = 120, which simplifies to -x + 150 = 120, or -x = -30. Therefore, x = 30. Thus, the number of oranges sold is 30.
Roberto is planning a weekend trip to the Piney Woods in East Texas. He wants to rent two types of cabins for his family: deluxe cabins that cost $150 per night and standard cabins that cost $90 per night. If Roberto rents a total of 5 cabins and spends $630 in total, how many deluxe cabins did he rent?
- 2
- 3 ✓
- 4
- 1
Why: Let x represent the number of deluxe cabins and y the number of standard cabins. The system of equations can be set up as: x + y = 5 (the total number of cabins) and 150x + 90y = 630 (the total cost). From the first equation, we can express y as y = 5 - x. Substituting y in the second equation gives us 150x + 90(5 - x) = 630, simplifying to 150x + 450 - 90x = 630. This simplifies to 60x + 450 = 630, leading to 60x = 180, so x = 3. Thus, Roberto rented 3 deluxe cabins.
Caroline is organizing a fundraiser for her school in Plano, Texas, selling cookies and brownies. She sells cookies for $2 each and brownies for $3 each. If she sells a total of 60 items and makes $120, which system of equations can be used to determine the number of cookies (x) and the number of brownies (y) she sold?
- x + y = 60, 2x + 3y = 120 ✓
- x + y = 120, 2x + 3y = 60
- x + y = 60, 2x + 3y = 60
- x + y = 120, 2x + 3y = 120
Why: The first equation x + y = 60 represents the total number of items sold (cookies and brownies), while the second equation 2x + 3y = 120 represents the total money earned from those sales. Therefore, the correct system of equations to model the situation is x + y = 60 and 2x + 3y = 120.
Camila is planning a trip from Amarillo to visit the Palo Duro Canyon. The distance from Amarillo to the canyon is 20 miles. She decides to rent a bicycle for her trip. The rental company charges a flat fee of $10 plus $2 per mile traveled. Camila discovers that she can also rent a scooter for a flat fee of $15 plus $1.50 per mile. If x represents the number of miles traveled, which system of equations can be used to find the point where the total cost of renting the bicycle equals the total cost of renting the scooter?
- 10 + 2x = 15 + 1.5x ✓
- 10 + 2x = 15 + 1.5x + 20
- 10x + 2 = 15 + 1.5x
- 10 + 2x = 20 + 15 + 1.5x
Why: The correct answer is 10 + 2x = 15 + 1.5x. This equation represents the total cost of renting the bicycle (10 + 2 times the number of miles x) set equal to the total cost of renting the scooter (15 + 1.5 times the number of miles x). This system of equations allows us to find the point where both costs are equal.
Common questions about TEKS A.5C
What is TEKS A.5C?
TEKS A.5C is a Algebra I Linear Functions, Equations, Inequalities standard from the Texas Essential Knowledge and Skills. The standard says: Solve systems of two linear equations with two variables for mathematical and real-world problems.
How many TEKS A.5C practice questions are available?
200+ practice questions tagged to TEKS A.5C. All free to print or practice online. We pull a fresh set each time you print a worksheet so your kid doesn't see the same questions twice.
What kind of questions test TEKS A.5C on the STAAR?
System of equations; substitution or elimination. TEKS A.5C is a high-cognitive-demand standard — multi-step reasoning is expected.
Where do these questions come from?
Generated by our AI pipeline, then independently quality-gated by two cross-vendor models (gpt-4o for content review, Claude Sonnet 4.5 for math verification) before publishing. Every question is tagged to TEKS A.5C and modeled on real STAAR item shapes. No typos, no wrong answer keys, no broken explanations.