Question

Solve the system of equations? 5=y-x 4x^2=-17x+y+4

Answer 1

Two pairs of solutions `(1/2,11/2)` and `(9/2,1/2)`

Explanation:

From the first equation: `y=5+x`
The substitution in the second one this value for `y` and
we have `4x^2+16x-9=0`

Apply the general formula for second degree equations
`ax^2+bx+c=0` that is `x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(-16+-sqrt(16^2-4·4·(-9)))/(2·4)=(-16+-20)/8=1/2 and 9/2`

If `x=1/2` then `y=11/2`

If `x=9/2` then `y=1/2`

The pair of solutions are the interception points between the straigh line `y=5+x` and the parabola `4x^2+17x-4=y`