System of the equations consists of a straight line and parabola will be [tex]y = x - 4[/tex] and [tex]y = x^{2} + 4[/tex].
What is system of equation?
" A system of equations is a finite set of equations for which we find the common solution."
According to the question,
Y - intercept of line = ( 0, -4)
X - intercept of line = ( 4 , 0)
Standard equation for straight line y = mx +c
m = slope
c = y - intercept
Slope of the line 'm' = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{0-(-4)}{4-0}[/tex]
= [tex]\frac{4}{4}[/tex]
= 1
y- intercept 'c' = - 4
Substitute the value to get the equation of line we get,
Equation of the line y = x - 4
For equation of parabola,
Standard equation of parabola y = (x-h)² + k
Vertex (h, k) = ( 0,2)
Substitute the value of the vertex we get,
y = (x-0)² + 2
⇒y = x² + 2
Hence, system of the equations consists of a straight line and parabola will be [tex]y = x - 4[/tex] and [tex]y = x^{2} + 4[/tex].
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