Solving Systems of Equations by Graphing Worksheet With Blank Grids

Two equations and a blank grid per problem, new systems with every New sheet, both lines drawn in the key.

Solving Systems of Equations by Graphing

Name Date Score / 4

Graph both lines of each system. The point where they cross is the solution.

  1. 1.

    y = −2x − 1
    y = x − 4

    xy−10−8−6−4−22468100−10−8−6−4−2246810

    solution

  2. 2.

    y = −3x + 7
    y = −1⁄5x − 7

    xy−10−8−6−4−22468100−10−8−6−4−2246810

    solution

  3. 3.

    y = x + 9
    y = 2⁄5x + 6

    xy−10−8−6−4−22468100−10−8−6−4−2246810

    solution

  4. 4.

    y = 1⁄5x − 3
    y = −2⁄5x − 6

    xy−10−8−6−4−22468100−10−8−6−4−2246810

    solution

Sheet CO5M1V · Made at homeroomtools.com

Answer key: Solving Systems of Equations by Graphing

  1. 1. (1, −3)

    xy−10−55100−10−5510

  2. 2. (5, −8)

    xy−10−55100−10−5510

  3. 3. (−5, 4)

    xy−10−55100−10−5510

  4. 4. (−5, −4)

    xy−10−55100−10−5510

Sheet CO5M1V · answer key · Made at homeroomtools.com

Scroll the preview to see every page. Paper copies fit US Letter and A4 and need no colour ink.

4 problems on one page, plus the answer key. Sheet CO5M1V.

On the sheet
Problems
Equations

Next step Next: parallel and perpendicular linesOne line at a time: graph y = mx + b first

Slope and line facts behind every answer key

Show the table

Every line on these sheets goes through grid points with whole-number coordinates, so a slope can be counted off the graph square by square. The key is worked out with whole-number arithmetic and every slope is given in lowest terms.

IdeaWhat it says
Sloperise over run: the change in y divided by the change in x, m = (y₂ − y₁) ÷ (x₂ − x₁)
Slope-intercept formy = mx + b, where m is the slope and b is the y-intercept, the point (0, b) where the line crosses the y-axis
Positive and negativea line that climbs from left to right has a positive slope; one that falls has a negative slope
Zero slopea horizontal line, y = b: it rises by nothing, however far it runs
Undefined slopea vertical line, x = a: its run is 0, and nothing can be divided by 0
From a tablepick any two rows: the difference of the y values over the difference of the x values, in the same order
Standard formAx + By = C. Put y = 0 to find the x-intercept, C ÷ A, and x = 0 to find the y-intercept, C ÷ B
From a point and a slopeput the point into y = mx + b and solve for b: b = y − mx

A short code sits at the foot of every sheet and of its answer key, so loose pages can be matched. The share link rebuilds that sheet, number for number: a key printed next week still fits the copies handed out today.

How it works

This solving systems of equations by graphing worksheet opens with 4 blank −10 to 10 grids, each under two equations. Students graph both lines and write where they cross; the key draws each pair and circles the point.

Read the full guide

Graphing systems of equations worksheet, two ways

Solve a system by graphing, lit at the start: two equations over a blank grid, with a blank for the solution. Read a solution off a graph: a graphs of systems of equations worksheet, where both lines are already drawn and students write the ordered pair. Its key adds the two equations, such as (2, −3): y = −5x + 7 and y = −x − 1.

Solving systems of linear equations graphically worksheet, special cases

Tick No solution and same-line systems and some pairs have no single crossing point. Parallel lines are keyed no solution. One line written twice, such as y = −5x + 6 and 2y = −10x + 12, is keyed infinitely many solutions.

  • To mix standard form into a graphing systems of linear equations worksheet, set Equations to Other forms too: 3x + y = 7 and x + 5y = −35.
  • Have students check an answer in both equations: (1, −3) gives −2 − 1 = −3 and 1 − 4 = −3.
  • A solve systems of equations by graphing worksheet of 4 fits one page; 6 or 8 print on 2.

Questions and answers

How do you solve a system of equations by graphing?

Graph both lines on one grid and find the point where they cross. That ordered pair makes both equations true, so it is the solution. Parallel lines give no solution, and two equations for the same line give infinitely many.

Is there a graphing systems of equations worksheet PDF?

Press Print and choose Save as PDF in your browser's print window. The blank grids come first. The answer key follows on its own page, with each solution beside a grid that shows both lines.

Does this solving systems of equations graphically worksheet have answers?

Yes. Every sheet ends with a key that lists each solution as an ordered pair, such as (5, −8). Untick Answer key after the sheet to print the problems alone.

Why is every solution a pair of whole numbers?

Each system is built from its crossing point, a grid point with whole-number coordinates, so students can read it off the graph exactly. Pairs of lines that cross at too shallow an angle to read with a ruler are never printed.

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