Simultaneous equations: solving with graphs

The Maths Habit

  1. Complete the table for y = 2x − 1.

    x−10123
    y−3−1135

  2. Where does the line x + y = 6 cross the axes?

    (0, 6) and (6, 0)

  3. Write the gradient and the y intercept of y = 3 − 2x.

    gradient −2, intercept 3

  4. Solve the simultaneous equations y = x + 2 and 2x + y = 14.

    x = 4, y = 6

  5. Is the point (3, 5) on the line y = 2x − 1?

    Yes: 2 × 3 − 1 = 5

xy01234567891011123456789101112y = x + 1y = 11 − x

What is the solution of y = x + 1 and y = 11 − x?

  1. Ax = 5, y = 6
  2. Bx = 6, y = 5
  3. Cx = 1, y = 11
  4. Dx = 5

A: x = 5, y = 6

Point of intersection
The point where two lines cross.
Solution
The values of x and y that make both equations true.

Solve y = 2x − 1 and x + y = 11 by drawing their lines for 0 ≤ x ≤ 6.

xy123456−11234567891011y = 2x − 1x + y = 11
x = 4
y = 7
Check in both equations
7 = 2 × 4 − 1 ✓4 + 7 = 11 ✓

Solve y = x + 1 and y = 9 − x by drawing their lines. The line y = x + 1 is drawn.

xy012345612345678910y = x + 1y = 9 − x
x = 4
y = 5
Check in both equations
5 = 4 + 1 ✓5 = 9 − 4 ✓

Solve y = 2x − 1 and x + y = 11 by drawing their lines for 0 ≤ x ≤ 6.

xy123456−11234567891011y = 2x − 1x + y = 11
x = 4
y = 7
Check in both equations
7 = 2 × 4 − 1 ✓4 + 7 = 11 ✓

Solve 2x + y = 4 and y = x − 5 by drawing their lines. Plot 2x + y = 4 from where it crosses the axes.

xy−112345−6−5−4−3−2−1123452x + y = 4y = x − 5
x = 3
y = −2
Check in both equations
2 × 3 + (−2) = 4 ✓(−2) = 3 − 5 ✓

Simultaneous equations: solving with graphs worksheet, questions 1 to 4

Draw y = 2x and x + y = 4. Use your graph to estimate the solution. Then find it exactly.

xy01234123456y = 2xx + y = 4
x ≈ 1.3
y ≈ 2.7
Exactly
x = 43
y = 83
Check in both equations
83 = 2 × 43 ✓43 + 83 = 4 ✓

Draw y = x + 2 and 2x + y = 3. Use your graph to estimate the solution. Then find it exactly.

xy−1012312345y = x + 22x + y = 3
x ≈ 0.3
y ≈ 2.3
Exactly
x = 13
y = 73
Check in both equations
73 = 13 + 2 ✓2 × 13 + 73 = 3 ✓

Draw y = 2x and x + y = 4. Use your graph to estimate the solution. Then find it exactly.

xy01234123456y = 2xx + y = 4
x ≈ 1.3
y ≈ 2.7
Exactly
x = 43
y = 83
Check in both equations
83 = 2 × 43 ✓43 + 83 = 4 ✓

Draw y = 4 − x and y = 2x + 2. Use your graph to estimate the solution. Then find it exactly.

xy−1012312345y = 4 − xy = 2x + 2
x ≈ 0.7
y ≈ 3.3
Exactly
x = 23
y = 103
Check in both equations
103 = 4 − 23 ✓103 = 2 × 23 + 2 ✓

Simultaneous equations: solving with graphs worksheet, questions 5 to 8

Answer sheet

  1. Draw y = 3x − 2 and 2x + 3y = 9. Use your graph to estimate the solution. Then find it exactly.

    x ≈ 1.4, y ≈ 2.1; x = 1511, y = 2311

  2. The lines y = x + 3, y = 9 − x and y = 3 make a triangle. Find its three corners, then its area.

    (0, 3), (3, 6), (6, 3); area 9

  1. Write down the solution of y = 2x − 1 and y = 8 − x.

    x = 3, y = 5
    xy234456

  2. Draw 2x + y = 9 on the grid with y = x + 3. Solve the simultaneous equations.

    x = 2, y = 5
    xy012345369y = x + 3

  3. Which is the best estimate of the solution of y = 2x + 1 and x + y = 5? A  x = 1, y = 4B  x = 1.3, y = 3.7
    C  x = 3.7, y = 1.3D  x = 1.5, y = 3 Then solve y = 2x + 1 and y = 3 − 2x by algebra.

    B; x = 12, y = 2
    xy01212345
Exit tickets to print