Solve the simultaneous equations.
3x + 5y = 24
x + 7y = 56
▶️ Answer/Explanation
Ans: x = −7, y = 9
From the second equation, express \( x \) as \( x = 56 – 7y \).
Substitute \( x = 56 – 7y \) into the first equation: \( 3(56 – 7y) + 5y = 24 \).
Simplify: \( 168 – 21y + 5y = 24 \) → \( -16y = -144 \) → \( y = 9 \).
Substitute \( y = 9 \) back into \( x = 56 – 7y \): \( x = 56 – 63 = -7 \).
(a) Solve the simultaneous equations.
You must show all your working.
4x + 2y = 31
6x – 2y = 34
(b) Factorise 14p2+ 21pq.
▶️ Answer/Explanation
(a) Ans: x = 6.5, y = 2.5
Add the two equations to eliminate \( y \): \( 4x + 2y + 6x – 2y = 31 + 34 \).
Simplify to \( 10x = 65 \), giving \( x = 6.5 \).
Substitute \( x = 6.5 \) into the first equation: \( 4(6.5) + 2y = 31 \).
Solve for \( y \): \( 26 + 2y = 31 \) → \( 2y = 5 \) → \( y = 2.5 \).
(b) Ans: 7p(2p + 3q)
Identify the greatest common factor (GCF) of \( 14p^2 \) and \( 21pq \), which is \( 7p \).
Factor out \( 7p \): \( 14p^2 + 21pq = 7p(2p + 3q) \).