ACT Math · Systems of equations

Solve the system by elimination: 4x + 3y = 25 and 2x - 3y = -1. What is the value of x + y?

Solve the system by elimination: 4x+3y=254x + 3y = 25 and 2x−3y=−12x - 3y = -1. What is the value of x+yx + y?

Answer and explanation

Answer: D: 7

Add the equations to eliminate yy: (4x+3y)+(2x−3y)=25+(−1)(4x+3y)+(2x-3y)=25+(-1), so 6x=246x=24 and x=4x=4. Substitute into 2x−3y=−12x-3y=-1: 8−3y=−18-3y=-1, so y=3y=3. Check in the first equation: 4(4)+3(3)=254(4)+3(3)=25. Then x+y=4+3=7x+y=4+3=7, choice D. Choice B (44) is xx alone, and the question asks for the sum. Choice A (11) is the difference y−xy-x with a sign slip or x−yx-y, and choice C (1212) is the product xyxy. Always reread what the question asks for after solving the system.

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