Question

Solve each system by graphing y > 5x + 1 and y ≤ -x + 3

Answer 1

EXPLANATION :

From the problem, we have the inequalities :

`\begin{gathered} y>5x+1 \\ y\le-x+3 \end{gathered}`

Take the symbols as "=" sign.

We need two points to graph the inequalities.

y = 5x + 1

when x = 0, the value of y is :

y = 5(0) + 1

y = 1

when y = -4, the value of x is :

-4 = 5x + 1

-4 - 1 = 5x

-5 = 5x

x = -1

So we have the points (0, 1) and (-1, -4)

The type of boundary line depends on the inequality symbol.

Since the symbol is ">", the boundary line is a dashed or broken line.

Determine the region by testing the origin (0, 0)

If (0, 0) satisfies the inequality, then the region will pass thru the origin.

y > 5x + 1

0 > 5(0) + 1

0 > 1

False

Since the result is NOT true, the region will NOT pass thru the origin.

The graph will be :

Next is to graph the second inequality :

y = -x + 3

when x = 0, the value of y is :

y = -0 + 3

y = 3

when y = 0, the value of x is :

0 = -x + 3

x = 3

The points are (0, 3) and (3, 0)

The boundary line is a solid line since the symbol is "≤"

Determine the region of the second inequality by testing again the origin (0, 0)

y ≤ -x + 3

0 ≤ -0 + 3

0 ≤ 3

True

Since the result is true, the region will pass thru the origin.

The graph will be :

The solution is the overlapping region between the two inequalities.