Simultaneous equations: multiply one equation

The Maths Habit

1Expand 3(2x − y + 4)6x − 3y + 122Work out −4 − (−9)53Solve 2x + y = 9 and 3x − y = 11x = 4, y = 1 (add)4Solve 5x + 3y = 21 and 2x + 3y = 12x = 3, y = 2 (subtract)

Add them. Subtract them. What happens?

(1)2x+3y=17
(2)3x+y=8
(1) + (2)
5x+4y=25nothing removed
(1) − (2)
−x+2y=9nothing removed

Neither removes a letter: no pair of coefficients matches.

Which pair needs one equation multiplied first?

A
(1)4x+3y=5
(2)4x−y=−7
B
(1)2x+5y=8
(2)6x+y=−4
C
(1)x+2y=2
(2)3x−2y=14

B. A: the x terms match, so subtract. C: the y terms are opposite, so add.

Multiply 3x + y = 7 by 2.

A 6x + 2y = 14B 6x + y = 14C 6x + 2y = 7D 6x + 2y = 9

A: every term is multiplied by 2, both sides.

Solve the simultaneous equations.

(1)2x+3y=17
(2)3x+y=8
(2) × 3
(3)9x+3y=24
(3) − (1)
7x=7
x=1
(2)3+y=8
y=5
x = 1,  y = 5
Check in (1): 2 + 15 = 17 ✓

Look first: do the coefficients already match? If so, do not multiply.

Solve the simultaneous equations.

(1)4x+3y=10
(2)2x−y=10
(2) × 3
(3)6x−3y=30
(1) + (3)
10x=40
x=4
(2)8−y=10
−y=2
y=−2
x = 4,  y = −2
Check in (1): 16 − 6 = 10 ✓

Solve the simultaneous equations.

(1)2x+3y=17
(2)3x+y=8
(2) × 3
(3)9x+3y=24
(3) − (1)
7x=7
x=1
(2)3+y=8
y=5
x = 1,  y = 5
Check in (1): 2 + 15 = 17 ✓

Look first: do the coefficients already match? If so, do not multiply.

Solve the simultaneous equations.

(1)2x+5y=1
(2)x+3y=1
(2) × 2
(3)2x+6y=2
(3) − (1)
y=1
(2)x+3=1
x=−2
x = −2,  y = 1
Check in (1): −4 + 5 = 1 ✓

Look first. Do you need to multiply? If so, which equation, and by what?

a
(1)5x+2y=9
(2)3x−2y=7
No multiplying: add.
b
(1)x+3y=10
(2)4x+5y=19
(1) × 4, to match x.
c
(1)2x+3y=8
(2)5x+6y=17
(1) × 2, to match y.
d
(1)3x−y=5
(2)2x+4y=22
(1) × 4, to match y.

Look first: do the coefficients already match? If so, do not multiply.

Simultaneous equations: multiply one equation worksheet, page 1

Answer sheet

  1. Solve 5x + 2y = 9 and 3x + 4y = 4.
    Which letter is quicker to eliminate? Why?

    y; x = 2, y = −12

  2. Three times a number plus a second number is 23.
    The first plus twice the second is 16.
    Find the two numbers.

    6 and 5

  3. Solve 0.5x + y = 5 and x + 3y = 13.

    x = 4, y = 3

  1. Multiply 2x − 5y = 3 by 3.

    6x − 15y = 9

  2. Solve the simultaneous equations.
    (1)3x+2y=10(2)3x−4y=7

    x = 3, y = 12

  3. Solve the simultaneous equations.
    (1)5x+2y=−1(2)x−4y=13

    x = 1, y = −3
Exit tickets to print