7
algebra

Solve by elimination: {2x+y=112xy=5\begin{cases} 2x + y = 11 \\ 2x - y = 5 \end{cases}

A

(3,5)(3, 5)

B

(5,1)(5, 1)

C

(4,3)(4, 3)

D

(2,7)(2, 7)

Correct Answer: C

Choice C is the correct answer. The yy terms are opposites, so we add the equations.

Step 1: Add the equations: (2x+y)+(2xy)=11+5(2x + y) + (2x - y) = 11 + 54x=164x = 16x=4x = 4

Step 2: Substitute x=4x = 4 into the first equation: 2(4)+y=112(4) + y = 118+y=118 + y = 11y=3y = 3

Solution: (4,3)(4, 3)

Verification: 2(4)3=83=52(4) - 3 = 8 - 3 = 5

💡 Strategic Tip: Elimination is fastest when coefficients already match or are opposites.

Choice A is incorrect because2(3)+5=6+5=112(3) + 5 = 6 + 5 = 11 ✓, but 2(3)5=65=1 eq52(3) - 5 = 6 - 5 = 1 \ eq 5.

Choice B is incorrect because2(5)1=101=9 eq52(5) - 1 = 10 - 1 = 9 \ eq 5.

Choice D is incorrect because2(2)+7=4+7=112(2) + 7 = 4 + 7 = 11 ✓, but 2(2)7=47=3 eq52(2) - 7 = 4 - 7 = -3 \ eq 5.