To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x − 4y = 6 −3x + 3y = 12 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Accepted Solution
A:
Answer:Option B is correct.add 4 times the second equation to 3 times the first equationStep-by-step explanation:Given the system of equation:[tex]2x - 4y = 6[/tex] ......[1][tex]-3x + 3y =12[/tex] .....[2]Multiply equation [1] by 3 we get;[tex]3(2x-4y) = 3 \cdot 6[/tex]Using distributive property; [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]6x - 12y = 18 .......[3]Multiply equation [2] by 4 we get;[tex]4(-3x+3y) = 4 \cdot 12[/tex]Using distributive property we get;-12x + 12y = 48 ......[4]Add equation [3] and [4] to eliminate y and solve for x;(6x -12y) + ( -12x +12y ) = 18 + 486x - 12y -12x + 12y = 66Combine like terms;6x - 12x = 66or-6x = 66 Simplify:x = -11Therefore, the operation which could be used to eliminate the y-variable and find the value of x is;add 4 times the second equation to 3 times the first equation.