what value of b will cause the system to have an infinite number of solutions?\ny = 6x + b\n-3x +…

what value of b will cause the system to have an infinite number of solutions?\ny = 6x + b\n-3x + \\frac{1}{2}y=-3

what value of b will cause the system to have an infinite number of solutions?\ny = 6x + b\n-3x + \\frac{1}{2}y=-3

Answer

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

Starting with $-3x+\frac{1}{2}y=-3$. Add $3x$ to both sides: $\frac{1}{2}y = 3x - 3$. Multiply through by 2 to get $y=6x - 6$.

Step2: Compare with the first equation

The first equation is $y = 6x + b$. For a system of linear equations $y=m_1x + c_1$ and $y=m_2x + c_2$ to have an infinite number of solutions, $m_1=m_2$ and $c_1 = c_2$. Here, $m_1=m_2 = 6$. So, for infinite solutions, $b=-6$.

Answer:

$-6$