5
algebra

Solve the system: {x=5y12x+3y=23\begin{cases} x = 5y - 1 \\ 2x + 3y = 23 \end{cases}

A

(9,2)(9, 2)

B

(4,1)(4, 1)

C

(14,3)(14, 3)

D

(6,1.4)(6, 1.4)

Correct Answer: A

Choice A is the correct answer. We use substitution since x=5y1x = 5y - 1 is already iStep 1: Substitute x=5y1x = 5y - 1 into 2x+3y=242x + 3y = 24: 2(5y1)+3y=242(5y - 1) + 3y = 2410y2+3y=2410y - 2 + 3y = 2413y=2613y = 26y=2y = 2

Step 2: Find xx using x=5y1x = 5y - 1: x=5(2)1=101=9x = 5(2) - 1 = 10 - 1 = 9

Solution: (9,2)(9, 2)

Verification: 2(9)+3(2)=18+6=242(9) + 3(2) = 18 + 6 = 24

💡 Strategic Tip: When x is isolated, substitute directly into the other equation.

Choice B is incorrect because2(4)+3(1)=8+3=11 eq242(4) + 3(1) = 8 + 3 = 11 \ eq 24.

Choice C is incorrect because2(14)+3(3)=28+9=37 eq242(14) + 3(3) = 28 + 9 = 37 \ eq 24.

Choice D is incorrect because6 eq5(1.4)1=71=66 \ eq 5(1.4) - 1 = 7 - 1 = 6.