For the general line equation

`y =m*x +n` (1)

the slope is `m` and the `y` intercept is `n`.

Thus the slope of the first line `y =-4x +3` is `m_1 =-4` .

For the second line we need to write it in the general form (1).

`4y +x =-1`

`4y =-x-1`

`y =(-1/4)*x -1/4`

Therefore the second line slope is `m_2 =-1/4` .

DEFINITION: two lines are perpendicular if their slopes are in the relation: `m_1*m_2 =-1` .

Since in our case `m_1*m_2 =(-4)*(-1/4) =+1` the two lines are not perpendicular.

**Answer: the two given lines are not pependicular**.

y = -4x + 3 ------eq(i)

4y + x = -1 ------eq(ii)

These simultaneous equations can be solved with the help of substitution method. In eq(i) it can be seen that the value of y is given which we can input in eq(ii) to find the value of x and after that y.

4y + x = -1

4(-4x + 3) + x = -1

-16x + 12 + x = -1

-15x + 12 = -1

-15x + 12 - 12 = -1 - 12 Subtract 12 from both sides

-15x = -13

-15x/-15 = -13/-15 Divide both sides by -15

**x = 13/15**

Now to find the value of y we need input the value of x in eq(i),

y = -4x + 3

y = -4(13/15) + 3

y = -52/15 + 3

y = -52/15 + 45/15 Taking LCD

**y = -7/15**

Now input both values in any equation to verify the answers,

y = -4x + 3

-7/15 = -4(13/15) + 3

-7/15 = -52/15 + 45/15

-7/15 = -7/15

LHS = RHS

proved.

**x = 13/15**

**y = -7/15 Answer.**

The set of equations y=-4x+3 and 4y+x=-1 has to be solved.

Substitute y = -4x + 3 in 4y + x = -1

4*(-4x + 3) + x = -1

-16x + 12 + x = -1

-15x = -13

x = 13/15

y = -4*(13/15) + 3 = -52/15 + 3 = (-52 + 45)/15

= -7/15

The solution of the given equations is x = 13/15 and y = -7/15