Question

This is the question

Answer 1

Given that

y = 1/4x + 4

x + y = -1

For the first equation,

Let us find the x intercept by making x equals to 0

`\begin{gathered} y\text{ = }(1)/(4)x\text{ + 4} \\ \text{let x = 0} \\ y\text{ = }(1)/(4)(0)\text{ + 4} \\ \text{y = 0 + 4} \\ \text{y = 4} \end{gathered}`

To find x, let y = 0

`\begin{gathered} y\text{ = }(1)/(`4)x\text{ + 4} \\ \text{y = }(x)/(4)\text{ + 4} \\ \text{Common denominator = 4} \\ y\text{ = }\frac{x\text{ + 16}}{4} \\ \text{Cross multiply} \\ 4y\text{ = x + 16} \\ \text{make y = 0} \\ 4(0)\text{ = x + 16} \\ \text{0 = x + 16} \\ x\text{ =-16} \end{gathered}`

Therefore, we have (0, 4) and (-16, 0)

For the second equation

x + y = -1

To find the x - intercept, make x = 0

0 + y = -1

y = -1

(0, -1)

To find x, let y = 0

x + y = -1

x + 0 = -1

x = -1

(-1, 0)

Therefore, the two points are (-1, 0) and (0, -1)

The above points can now be graph

The diagram above is just an illustration on how to graph the given points

From the numbered graph, their point of intersection is (-4, 3)

x = -4 and y = 3