Algebra 1 Systems of Linear Equations Worksheets with Answers (Free PDF)

Algebra 1 systems of equations worksheet – Maths PDF

Cover of the book Algebra 1 Math Worksheets with Answers (PDF)

Download as a PDFThe Algebra 1 worksheets book with answersPrintable PDFSee the book ›

Sommaire

This algebra 1 systems of equations worksheet covers systems of linear equations (Common Core A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3), with a free PDF to print.

Key takeaway: This worksheet helps Algebra 1 students practice all three methods for solving systems and learn to choose one.

Topic: Systems of Linear Equations (Algebra 1)
Content: 21 worksheet problems, from easy to challenging
Standards: A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps Algebra 1 students practice all three methods for solving systems and learn to choose one. Also, the problems begin with checking a solution and finish with real situations.

There are 21 worksheet problems. Worksheet problem 1 checks a solution, and worksheet problems 2 and 3 graph. Worksheet problems 4 and 5 count solutions without graphing. Also, worksheet problems 6 to 9 use substitution. Worksheet problems 10 to 12 use elimination with matching coefficients, and worksheet problems 13 to 15 multiply first or find special cases. Worksheet problems 16 to 21 model theater tickets, coins, two gyms, a bake sale, a boat in a current, and two numbers. Allow about 55 minutes.

These 20 problems practice systems of linear equations (Common Core A-REI.C.5, A-REI.C.6, and A-REI.D.11). You will solve systems by graphing, substitution, and elimination, recognize no solution and infinitely many solutions, and model real problems with two equations. The first problems are short skill checks, and the last six are word problems that need several steps. Work in order and show every line of your work, because a bare answer earns little credit on a test.

Algebra 1 · Common Core State Standards: A-REI.C.5, A-REI.C.6, A-REI.D.11, A-CED.A.3

Algebra 1 systems of equations worksheet: worksheet problems 1 to 10

1 – Check a solution

First, determine whether $(2, 3)$ is a solution of the system $y = x + 1$ and $y = -x + 5$.

2 – Solve by graphing

Graph of both lines.

Next, solve the system by graphing: $y = 2x – 1$ and $y = -x + 5$.

3 – Graph and read

Two lines.

Then, solve the system by graphing: $y = x + 4$ and $y = -2x + 1$.

4 – Parallel lines

Without graphing, decide how many solutions the system has: $y = 3x + 2$ and $y = 3x – 4$.

5 – Same line

Also, how many solutions does the system $y = 2x + 1$ and $2y = 4x + 2$ have?

6 – Substitution with y = 3x

First, solve by substitution: $y = 3x$ and $x + y = 12$.

7 – Substitution with x

Next, solve by substitution: $x = 2y – 1$ and $3x + y = 11$.

8 – Two slope-intercept equations

Then, solve: $y = -x + 7$ and $y = 2x + 1$.

9 – Substitution after rearranging

Now, solve: $2x + y = 10$ and $3x – y = 5$.

10 – Elimination by adding

Also, solve by elimination: $x + y = 14$ and $x – y = 6$.

Worksheet problems 11 and up

11 – Elimination with opposites

First, solve by elimination: $2x + 3y = 12$ and $4x – 3y = 6$.

12 – Elimination by subtracting

Next, solve by elimination: $3x + 2y = 16$ and $x + 2y = 8$.

13 – Multiply one equation

Then, solve: $2x + 3y = 13$ and $5x – 2y = 4$.

14 – Multiply both equations

Now, solve: $3x – 4y = 1$ and $2x + 3y = 12$.

15 – Elimination gives no solution

Also, solve: $2x + 4y = 8$ and $x + 2y = 10$.

16 – Movie tickets

Ticket prices.

First, a theater sells adult tickets for $9 and student tickets for $6. Eight tickets cost $60. Write and solve a system for the number of adult tickets $a$ and student tickets $s$.

17 – Coins

Coin values.

Aisha has 18 coins, all dimes and quarters, worth $3.00 in total. Write and solve a system for the number of dimes $d$ and quarters $q$.

18 – Two gyms

Two gym prices.

Gym A charges a $30 joining fee plus $20 per month. Gym B has no joining fee and charges $35 per month. Write a system and find when the total costs are equal.

19 – Bake sale

Now, at a bake sale, Noah sells 40 items, cookies at $1.50 and muffins at $2.50, for $70 in all. Find the number of cookies $c$ and muffins $m$.

Worksheet problem 20 and after

20 – Boat and current

Also, a boat travels 24 miles downstream in 2 hours and returns upstream in 3 hours. Find the boat’s speed $b$ in still water and the current’s speed $c$ in miles per hour.

21 – Number problem

First, the sum of two numbers is 42. One number is 6 more than twice the other. Find the numbers.

Key facts behind this algebra 1 systems of equations worksheet

Key facts

A solution of a system is an ordered pair that satisfies every equation.
Graphing: the solution is the intersection point of the lines.
Substitution: solve one equation for a variable and substitute into the other.
Elimination: add or subtract equations to cancel a variable.
Parallel lines give no solution; identical lines give infinitely many.

Common mistakes with this algebra 1 systems of equations worksheet

Students solve, get a strange result, and assume they made an error. However, the variables may cancel, which signals parallel lines or the same line.
Students mix units in a value equation. Instead, write all amounts in the same unit, such as cents, before you set up the totals.
Students ignore the current in a boat problem. Because the current helps in one direction and hurts in the other, add it for downstream and subtract it for upstream.

Tips before you start the worksheet problems

In worksheet problem 18, solve the system and also graph it. Seeing the crossing point helps you explain when each gym is cheaper.
For word problems, first write what each variable stands for. Then build the equations, because a clear definition makes a wrong setup easy to spot.
Teachers can ask students to solve worksheet problem 19 in two ways and compare the work.

Download the algebra 1 systems of equations worksheet as a PDF with the button below and keep it with your notes.

Algebra 1 systems of equations worksheet: frequently asked questions

How do you write a system for a ticket problem?

Write one equation for the number of tickets and one for the money. With tickets at 5 dollars and 3 dollars, 10 tickets sold, and 38 dollars collected, the system is a + s = 10 and 5a + 3s = 38.

How do you solve a boat in a current problem?

Write the downstream speed as the boat speed plus the current, and the upstream speed as the boat speed minus the current. Then use distance equals rate times time for each trip, and solve the two equations.

How do you find when two plans cost the same?

Set the two cost equations equal, or solve the system, and find the number of months where the costs match. For example, a 10 dollar fee plus 5 per month and a flat 8 per month match at about 3.3 months.

All Algebra 1 chapters: Algebra 1 math.

Voter.. post

Free printable PDF