6
algebra

Solve the system: {y=2x+53xy=1\begin{cases} y = 2x + 5 \\ 3x - y = 1 \end{cases}

A

(8,21)(8, 21)

B

(4,13)(4, 13)

C

(6,17)(6, 17)

D

(5,15)(5, 15)

Correct Answer: C

Choice C is the correct answer. We use substitution since y=2x+5y = 2x + 5 is already isolated.

Step 1: Substitute y=2x+5y = 2x + 5 into 3xy=13x - y = 1: 3x(2x+5)=13x - (2x + 5) = 13x2x5=13x - 2x - 5 = 1x5=1x - 5 = 1x=6x = 6

Step 2: Find yy using y=2x+5y = 2x + 5: y=2(6)+5=12+5=17y = 2(6) + 5 = 12 + 5 = 17

Solution: (6,17)(6, 17)

Verification: 3(6)17=1817=13(6) - 17 = 18 - 17 = 1

💡 Strategic Tip: When one equation is solved for y, substitute into the other equation.

Choice A is incorrect because3(8)21=2421=3 eq13(8) - 21 = 24 - 21 = 3 \ eq 1.

Choice B is incorrect because3(4)13=1213=1 eq13(4) - 13 = 12 - 13 = -1 \ eq 1.

Choice D is incorrect because3(5)15=1515=0 eq13(5) - 15 = 15 - 15 = 0 \ eq 1.