Equations I — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Subtract 7 from both sides, then divide by 3: (22 − 7) ÷ 3.

x = 5

Question 2

(a)Add the two equations to eliminate y: (2x+y)+(x−y) = 11+1, giving 3x = 12, so x = 4. Substitute into x−y=1 to find y = 3.

x = 4, y = 3

Question 3

(a)Collect x terms on one side, numbers on the other: 5x−2x=9+3.

3x = 12, x = 4

Question 4

(a)From the second equation, x = y+2. Substitute into the first: 3(y+2)+2y=16.

5y+6=16, y=2, so x=4

Question 5

(a)Expand both sides: 2x−6 = 3x+3, then collect terms.

−9 = x, so x = −9

Question 6

(a)Subtract 3 from both sides, then multiply by 4.

x/4 = 4, so x = 16

Question 7

(a)Substitute y=x+1 into the second equation: 2x+(x+1)=10.

3x=9, x=3, y=4

Question 8

(a)Let the number be n: n + 7 = 2n − 3.

10 = n, so the number is 10

Question 9

(a)Collect x terms and numbers.

8 = 2x, x = 4

Question 10

(a)Expand both sides: 3x+6 = 2x+10, then collect terms.

x = 4

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