Solve the simultaneous linear equations: $x + 2 y = 5$ and $3 x - y = 4$

hard 3 marks Class 7 · Mathematics · Simple Equations

Answer

x=13/7, y=11/7

The correct answer is x=13/7, y=11/7 — Check both equations to confirm the solution.

Step-by-step solution

Multiply the first equation by 3 to align the $x$ terms: $3 x + 6 y = 15$ .
Subtract the second equation from this result to eliminate $x$ : $(3 x + 6 y) - (3 x - y) = 15 - 4$ .
Simplify the left side: $6 y - (- y) = 7 y$ ; right side: $11$ .
Solve for $y$ : $7 y = 11$ gives $y = \frac{11}{7}$ .
Substitute $y$ into the first original equation: $x + 2 (\frac{11}{7}) = 5$ .
Simplify: $x + \frac{22}{7} = 5$ which yields $x = 5 - \frac{22}{7} = \frac{35}{7} - \frac{22}{7} = \frac{13}{7}$ .
Check both equations to confirm the solution.

Common mistake: Using substitution incorrectly or not simplifying fractions properly

Concept tested: Solving simultaneous linear equations