alliicSelect the equations that are equivalent to the equation y+5 = -3(x-1)Select All that applyy = -3x - 2 y = -4x -53x + y = -2-4x + y = - 5
Accepted Solution
A:
first, we need to solve the first equation in order to see what the options need to be equivalent to. our first step to solving this is to distribute -3 through the parenthesis y + 5 = -3x + 3 next, move the constant to the right side and change its sign y = -3x + 3 - 5 calculate the difference y = -3x - 2 since we cant find x, your final solution for y is y = -3x - 2, x ∈ R now that we know the solution to that equation, we can now solve the options listed to see which ones are equivalent. first is y = -3x - 2, which is very simple to solve because y has already been found. since we know y and there is no solution for x, our answer to this equation is y = -3x -2, x ∈ R. since this is the exact same answer as our first equation, we know that the A is equivalent to y + 5 = -3(x - 1) the next equation is also already solved for y and has no x, so the answer to this equation is y = -4x - 5, x ∈ R. since this is does not have the same answer that y + 5 = -3(x - 1) had, option B is not equivalent. our next equation is 3x + y = -2 does not provide y for us, so we must solve it. first, you need to move the variable to the right side and change its sign 3x = -2 - y now divide both sides of the equation by 3 x = - 2/3 = y/3 write all the numerators above their common denominators x = - 2 + y/3 since we dont know what y is, our final solution is x = - [tex] \frac{2+y}{3} [/tex] , y ∈ R since this answer does not match the answer we are looking for, option C is not equivalent. finally, we must solve -4x + y = -5 the first step to solving this is to move the variable to the right side and change its sign -4x = -5 - y divide both sides of the equation by -4 x = 5/4 + y/4 now, write all the numerators above their common denominators x = 5 + y/4 since we dont know what y is, our answer is x = [tex] \frac{5+y}{4} [/tex] , y ∈ R since this is also not equivalent to y + 5 = -3(x - 1), our only answer is option A. let me know if you have any further questions :)