the diagram shows graphs of y=1/2x+2 and 2y+2x=12. Use the diagram to solve the simultaneous equations

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fieryanswererft fieryanswererft · Answer 1 · 2022-06-12T10:34:32+02:00

Answer: (2.67, 3.33)

Explanation:

For the function y = 1/2x + 2

[tex]\hrulefill[/tex]

For the function 2y + 2x = 12

Draw lines through these coordinates to produce a straight linear graph.

Then see, where they intersect each other. Intersection point : (2.67, 3.33)

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Аноним Аноним · Answer 2 · 2022-06-18T18:56:47+02:00

Answer:

[tex]\mathsf {(2.66, 3.33)}[/tex]

Step-by-step explanation:

[tex]\textsf {Given :}[/tex]

[tex]\mathsf {1) y = \frac{1}{2}x + 2}[/tex]

[tex]\mathsf {2) 2y + 2x = 12} \implies \mathsf {y + x = 6} \implies \mathsf {y = -x + 6}[/tex]

[tex]\mathsf{Solving :}[/tex]

[tex]\textsf {Equating the values of y from both equations :}[/tex]

[tex]\implies \mathsf {\frac{1}{2}x + 2 = -x + 6}[/tex]

[tex]\implies \mathsf {\frac{3}{2}x = 4}[/tex]

[tex]\implies \mathsf {3x = 8}[/tex]

[tex]\implies \mathsf {x = \frac{8}{3} \implies {x = 2.66...}}[/tex]

[tex]\textsf {Finding y :}[/tex]

[tex]\implies \mathsf {y = -\frac{8}{3} + 6}[/tex]

[tex]\implies \mathsf {y = \frac{18 - 8}{3}}[/tex]

[tex]\implies \mathsf {y = \frac{10}{3}} \implies \mathsf {y = 3.33...}[/tex]

[tex]\textsf {Graph of equations is attached below.}[/tex]