Question

graph the solution to the following system of inequalities.\

$$\begin{cases}7x + 5y < 30\\\\x \\geq 0\\\\y \\geq 0\\end{cases}$$

Explanation:

Answer:

Graph the line \(7x + 5y=30\) as a dashed line (since the inequality is \(7x + 5y\lt30\)). Find the intercepts: when \(x = 0\), \(y=6\); when \(y = 0\), \(x=\frac{30}{7}\approx4.29\). Shade the region below this line. Also, shade the region \(x\geq0\) (to the right of the \(y\)-axis) and \(y\geq0\) (above the \(x\)-axis). The solution is the intersection of these regions (in the first - quadrant below the line \(7x + 5y = 30\)).