Question

Solve the following system of equations for z and for y: System of Equations: Value of z Value of y y-8+22 y- 56- 6z Solve the following system of equations for a and for b: System of Equations: Value of aValue of ib 4а + 2b 20 15a +5b60 Plot the following system of equations on the following graph. System of Equations: p 1+q

Answer 1

Given system y = 8 + 2z ---- (i) y = 56 - 6z - (ii) substitute (ii) in (i) we obtain 56 - 6z = 8 + 2z Rightarrow - 6z - 2z = 8 - 56 Rightarrow - 8z = -48 Rightarrow z = 6 use this in any of (i) or (ii) we obtain y = 8 + 2(6) Rightarrow y = 8 + 12 Rightarrow y = 20 Given system 4a + 2b = 20 Rightarrow (i) 15a + 5b = 60 Rightarrow (ii) from (i) we have 4a = 20 - 2b Rightarrow a = 20 - 2b/4 Rightarrow (iii) substitute this in (ii) we get 15 (20 - 2b/4) + 5b = 60 Rightarrow 15 (10 - b)/2 + 5b = 60 Rightarrow 150 - 15b + 10b = 120 Rightarrow - 5b = -30 Rightarrow b = 6 use value of (b) in (iii) we get a = 20 - 2 (6)/2
It can be seen from the graph

The value of p=8/3 and

Value of q=5/3