Answer:
[tex]j=10-3k[/tex]
[tex]y = 2x - 7[/tex]
Step-by-step explanation:
Solving (a):
Given
[tex]\frac{3j + k}{2}=15-4k[/tex]
Required: Prove [tex]j=10-3k[/tex]
[tex]\frac{3j + k}{2}=15-4k[/tex]
Multiply through by 2
[tex]2 * \frac{3j + k}{2}=(15-4k) * 2[/tex]
[tex]3j + k = 30 - 8k[/tex]
Subtract k from both sides
[tex]3j = 30 - 9k[/tex]
Divide through by 3
[tex]j = \frac{30 - 9k}{3}[/tex]
j = 10 - 3k
Solving (b):
Given
[tex]5x - 2y = x+ 14[/tex]
Required
Prove: [tex]y = 2x - 7[/tex]
[tex]5x - 2y = x+ 14[/tex]
Subtract 5x from both sides
[tex]-2y = x - 5x + 14[/tex]
[tex]-2y = -4x + 14[/tex]
Divide through by -2
[tex]\frac{-2y}{-2} = \frac{-4x}{-2} + \frac{14}{-2}[/tex]
[tex]y = 2x - 7[/tex]
