which value, when placed in the box, would result in a system of equations with infinitely many solutions? y…
which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x + 4 6x + 3y = □ -12 -4 4 12
Answer
Explanation:
Step1: Rewrite first - equation in standard form
Given $y=-2x + 4$, rewrite it as $2x+y=4$. Multiply this equation by 3 to get $6x + 3y=12$. $3(2x + y)=3\times4$ $6x+3y = 12$
Step2: Analyze for infinite solutions
A system of linear equations $a_1x+b_1y=c_1$ and $a_2x + b_2y=c_2$ has infinitely many solutions when $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$. For the equations $6x + 3y=\square$ and $6x+3y = 12$, when the box is 12, the two equations are the same and the system has infinitely many solutions.
Answer:
12