Q. Which ordered pair is a solution of the equation?−3x+5y=2x+3yChoose 1 answer:(A) Only (2,4)(B) Only (3,3)(C) Both (2,4) and (3,3)(D) Neither
Combine Like Terms: First, we need to simplify the equation by combining like terms. We can do this by moving all terms involving x to one side of the equation and all terms involving y to the other side.−3x+5y=2x+3y
Move x and y Terms: Subtract 2x from both sides to get all the x terms on one side.−3x−2x+5y=3y
Subtract 2x: Combine the x terms.−5x+5y=3y
Combine x Terms: Now, subtract 3y from both sides to get all the y terms on one side.−5x+5y−3y=0
Subtract 3y: Combine the y terms.−5x+2y=0
Combine y Terms: Now we have a simplified equation: −5x+2y=0. We can check each ordered pair to see if it satisfies this equation.
Simplified Equation: Let's check the ordered pair (2,4).Substitute x=2 and y=4 into the equation.−5(2)+2(4)=0−10+8=0−2=0This ordered pair does not satisfy the equation.
Check (2,4): Now let's check the ordered pair (3,3). Substitute x=3 and y=3 into the equation. −5(3)+2(3)=0−15+6=0−9=0 This ordered pair also does not satisfy the equation.
Check (3,3): Since neither (2,4) nor (3,3) satisfy the equation −5x+2y=0, the correct answer is (D) Neither.
More problems from Does (x, y) satisfy the linear equation?