x−3y=8y2=x−4y−2If (x,y) is a solution to the system of equations shown, which of the following are y-coordinates of the solutions?Choose 1 answer:(A) −1 and −3(B) 14 and 2(C) −2 and 3(D) 2 and −3
Q. x−3y=8y2=x−4y−2If (x,y) is a solution to the system of equations shown, which of the following are y-coordinates of the solutions?Choose 1 answer:(A) −1 and −3(B) 14 and 2(C) −2 and 3(D) 2 and −3
Solve for x: Solve the first equation for x.The first equation is x−3y=8. To solve for x, add 3y to both sides of the equation.x=3y+8
Substitute into second equation: Substitute the expression for x into the second equation.The second equation is y2=x−4y−2. Substitute x with 3y+8.y2=(3y+8)−4y−2
Simplify the equation: Simplify the equation.Combine like terms on the right side of the equation.y2=3y+8−4y−2y2=−y+6
Rearrange for quadratic equation: Rearrange the equation to form a quadratic equation.Add y to both sides and subtract 6 from both sides to set the equation to zero.y2+y−6=0
Factor the quadratic equation: Factor the quadratic equation.We need to find two numbers that multiply to −6 and add up to 1. These numbers are 3 and −2.(y+3)(y−2)=0
Solve for y: Solve for y.Set each factor equal to zero and solve for y.y+3=0 or y−2=0y=−3 or y=2
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