Choice C is the correct answer. We'll use elimination. Let's eliminate $y$ by multiplying the first equation by 2.

Step 1: Multiply the first equation by 2: $2(5x - 2y) = 2(8)$$10x - 4y = 16$

Step 2: Add to the second equation: $(10x - 4y) + (3x + 4y) = 16 + 26$$13x = 42$$x = \frac{42}{13}$

This gives non-integer. - First: $5(3) - 2(3.5) = 15 - 7 = 8$ ✓

• Second: $3(3) + 4(3.5) = 9 + 14 = 23 \ eq 26$

$3(3) + 4(3.5) = 9 + 14 = 23$

Step 1: Multiply the first equation by 2: $10x - 4y = 16$

Step 2: Add to the second equation: $13x = 39$$x = 3$

Step 3: Substitute $x = 3$ into the first equation: $5(3) - 2y = 8$$15 - 2y = 8$$-2y = -7$$y = 3.5$

Solution: $(3, 3.5)$

Verification: $3(3) + 4(3.5) = 9 + 14 = 23$ ✓

💡 Strategic Tip: Multiplying to eliminate requires identifying which variable has easier coefficients to match.

Choice A is incorrect because$5(4) - 2(6) = 20 - 12 = 8$ ✓, but $3(4) + 4(6) = 36 \ eq 23$.

Choice B is incorrect because$5(2) - 2(1) = 10 - 2 = 8$ ✓, but $3(2) + 4(1) = 10 \ eq 23$.

Choice D is incorrect because$5(1) - 2(-1.5) = 5 + 3 = 8$ ✓, but $3(1) + 4(-1.5) = -3 \ eq 23$.