Question

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

Answer 1

Answer:

$\mathsf {(2.66, 3.33)}$

Step-by-step explanation:

$\textsf {Given :}$

$\mathsf {1) y = \frac{1}{2}x + 2}$

$\mathsf {2) 2y + 2x = 12} \implies \mathsf {y + x = 6} \implies \mathsf {y = -x + 6}$

$\mathsf{Solving :}$

$\textsf {Equating the values of y from both equations :}$

$\implies \mathsf {\frac{1}{2}x + 2 = -x + 6}$

$\implies \mathsf {\frac{3}{2}x = 4}$

$\implies \mathsf {3x = 8}$

$\implies \mathsf {x = \frac{8}{3} \implies {x = 2.66...}}$

$\textsf {Finding y :}$

$\implies \mathsf {y = -\frac{8}{3} + 6}$

$\implies \mathsf {y = \frac{18 - 8}{3}}$

$\implies \mathsf {y = \frac{10}{3}} \implies \mathsf {y = 3.33...}$

$\textsf {Graph of equations is attached below.}$

Answer 2

Answer: (2.67, 3.33)

Explanation:

For the function y = 1/2x + 2

• y-intercept = (0, 2)

• x-intercept = (-4, 0)

$\hrulefill$

For the function 2y + 2x = 12

• y-intercept = (0, 6)

• x-intercept = (6, 0)

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

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