Question

Solve the following pairs of linear equations : $3x - 5y = 4$, $9x = 2y + 7$

Hint:

Substitution would also be efficient here by substituting $9x$ from Eq. 2 into a tripled version of Eq. 1.

Answer 1

Step 1: Understanding the Concept:
We can use the elimination method or substitution method. Let's rewrite the equations in standard form $ax + by = c$.
Step 2: Standardizing and Equating:
(1) $3x - 5y = 4$ (2) $9x - 2y = 7$ Multiply Eq. (1) by 3 to eliminate $x$: \[ 9x - 15y = 12 \]
Step 3: Subtracting the Equations:
\[ (9x - 15y) - (9x - 2y) = 12 - 7 \] \[ -13y = 5 \implies y = -\frac{5}{13} \]
Step 4: Finding x and Final Answer:
Substitute $y = -5/13$ into Eq. (1): \[ 3x - 5(-\frac{5}{13}) = 4 \] \[ 3x + \frac{25}{13} = 4 \implies 3x = \frac{52-25}{13} = \frac{27}{13} \] \[ x = \frac{9}{13} \] The solutions are x = 9/13, y = -5/13.