1
algebra

Solve using substitution: {y=2x74x3y=5\begin{cases} y = 2x - 7 \\ 4x - 3y = 5 \end{cases}

A

(8,9)(8, 9)

B

(5,3)(5, 3)

C

(7,7)(7, 7)

D

(6,5)(6, 5)

Correct Answer: A

Choice A is the correct answer. Since y=2x7y = 2x - 7 is already isolated, substitute directly into the second equation.

Step 1: Substitute y=2x7y = 2x - 7 into 4x3y=54x - 3y = 5: 4x3(2x7)=54x - 3(2x - 7) = 54x6x+21=54x - 6x + 21 = 52x+21=5-2x + 21 = 52x=16-2x = -16x=8x = 8

Step 2: Find yy: y=2(8)7=167=9y = 2(8) - 7 = 16 - 7 = 9

Solution: (8,9)(8, 9)

Verification: 4(8)3(9)=3227=54(8) - 3(9) = 32 - 27 = 5

💡 Strategic Tip: When y is isolated, substitution eliminates the need for algebraic manipulation of the first equation.

Choice B is incorrect because4(5)3(3)=209=11 eq54(5) - 3(3) = 20 - 9 = 11 \ eq 5.

Choice C is incorrect because4(7)3(7)=2821=7 eq54(7) - 3(7) = 28 - 21 = 7 \ eq 5.

Choice D is incorrect because4(6)3(5)=2415=9 eq54(6) - 3(5) = 24 - 15 = 9 \ eq 5.