1
algebra

Solve using substitution: {y=4x35x+2y=37\begin{cases} y = 4x - 3 \\ 5x + 2y = 37 \end{cases}

A

(4,13)(4, 13)

B

(5,17)(5, 17)

C

(3,9)(3, 9)

D

(6,21)(6, 21)

Correct Answer: C

Choice C is the correct answer. Since y=4x3y = 4x - 3 is already isolated, substitute directly.

Step 1: Substitute into second equation: 5x+2(4x3)=375x + 2(4x - 3) = 375x+8x6=375x + 8x - 6 = 3713x=4313x = 43x=4313x = \frac{43}{13}

Non-integer. - First: 9=4(3)3=123=99 = 4(3) - 3 = 12 - 3 = 9

  • Second: 5(3)+2(9)=15+18=33 eq375(3) + 2(9) = 15 + 18 = 33 \ eq 37

💡 Strategic Tip: When one equation is y = ..., substitution is natural.

Choice A is incorrect because5(4)+2(13)=46 eq335(4) + 2(13) = 46 \ eq 33.

Choice B is incorrect because5(5)+2(17)=59 eq335(5) + 2(17) = 59 \ eq 33.

Choice D is incorrect because5(6)+2(21)=72 eq335(6) + 2(21) = 72 \ eq 33.