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PilotLPTM [1.2K]
2 years ago
6

1) Graph both equation and identify the point of intersection. y=2x+3 x+2y=8

Mathematics
1 answer:
Verizon [17]2 years ago
5 0

Answer:

Intersection Point: (0.4, 3.8)

General Formulas and Concepts:

<u>Algebra I</u>

  • Solving systems of equations by graphing

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = 2x + 3

x + 2y = 8

<u>Step 2: Graph</u>

<em>Where the 2 lines intersect is the solution set to the systems of equations.</em>

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Step-by-step explanation:

y=x^2-7x+4\\\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\\\mathrm{The\:parabola\:params\:are:}\\a=1,\:b=-7,\:c=4\\x_v=-\frac{b}{2a}\\x_v=-\frac{\left(-7\right)}{2\cdot \:1}\\\mathrm{Simplify}\\x_v=\frac{7}{2}\\\mathrm{Plug\:in}\:\:x_v=\frac{7}{2}\:\mathrm{to\:find\:the}\:y_v\:\mathrm{value}\\y_v=\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4\\

\mathrm{Simplify\:}\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4:\quad -\frac{33}{4}\\y_v=-\frac{33}{4}\\Therefore\:the\:parabola\:vertex\:is\\\left(\frac{7}{2},\:-\frac{33}{4}\right)\\\mathrm{If}\:a0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\\a=1\\\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)

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