Solving Linear Systems by Substitution 
Solve the following systems of linear equations and clearly state what the
point of intersection is
Show ALL of your work

a) 3 x+ y=7
−x+2 y=7

b) y=7 x+3
x−y=3

c) 2 x+3 y=8
x−2 y=−3

Question 5

A firm has the following linear total revenue 𝑅(𝑥) and total cost 𝐶(𝑥) functions. • 𝑅(𝑥) = 55𝑥

[4 marks]

• 𝐶(𝑥)=30𝑥+250

Find the break-even point for the firms.

Hint:

(1) find the profit function, setting it equal to zero, and solving for 𝑥, (2) setting 𝑅(𝑥) = 𝐶(𝑥) and solving for 𝑥, and
(3) graphing 𝑅(𝑥) and 𝐶(𝑥) and find the point of intersection.

2 38. Use Gauss-Jordan Elimination to solve the system of linear equations marks + y + 2x = 1 2.0 + 2y + 4z = 2 - - y - 22 = -1 Express your answer in vector form. Show your work.

Solve the following linear equations
a) 2r/7 = −4 b) 3x/4 = 15 c) x+3=5
d) 21= 3t e) t/12 − 1 = 1 f) 9 = 7 − 2 y
g) a/8 −3 = 7 h) 14 = 7k/5
i) 3w − 2 = 2w + 3
j) 6 − 5 k = 4 + 3 k k) 6t − 7 = 2 t + 5
l) 3 (x+6) = 2(x−1)

m) x −  2 / 2 +   x + 3 / 3 =10