Solve the following simultaneous equations: x + y = \(\frac{3}{2}\), x - y = \(\frac{5}{2}\)....

Solve the following simultaneous equations: x + y = \(\frac{3}{2}\), x - y = \(\frac{5}{2}\). And use your result to find the value of 2y + x.

x + y = \(\frac{3}{2}\), x - y = \(\frac{5}{2}\)

x + y = \(\frac{3}{2}\),

Multiply through by 2

2x + 2y = 3 ---------------- 1

x - y = \(\frac{5}{2}\)

Multiply through by 2

2x - 2y = 5 --------------- 2

Add eqn (1 and 2)

4x = 8

x = \(\frac{8}{4}\) = 2

Put x = 2 into either Eqn 1 or Eqn 2

2x - 2y = 5 --------------- 2

2(2) - 2y = 5

4 - 2y = 5

- 2y = 5 - 4 = 1

y = -\(\frac{1}{2}\)

2y + x. = 2 x -\(\frac{1}{2}\) + 2

= -1 + 2 = 1.

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