Answer:
System 1: x = -7; y = -7
System 2: No solution
Step-by-step explanation:
We can solve both system of equations by the method of elimination.
System 1
[tex]\begin{array}{lrcrl}(1)&-8x + 5y & = & 21 &\\(2)& -x + y & = & 0 &\\(3)&-5x + 5y &=&0&\text{Multiplied (2) by 5}\\(4)&3x & = & -21 & \text{Subtracted (1) from (3)}\\(5)&x & = &\mathbf{-7} & \text{Divided (4) by 3}\\(6)& 7+ y & = & 0 &\text{Substituted (5) into (2)}\\&y & = & \mathbf{-7} &\text{Subtracted 7 from each side}\\\end{array}[/tex]
The solution is x = -7, y = -7.
System 2
[tex]\begin{array}{lrcrl}(1)&7x + y & = & -6 &\\(2)& -21x - 3y & = & 4 &\\(3)&21x +3y &=&-18&\text{Multiplied (1) by 3}\\(4)&0 & = & -14& \text{Added (2) and(3)}\\\end{array}[/tex]
This is IMPOSSIBLE. There is NO SOLUTION.
You can write the two equations as
(1) 7x + y = -6
(2) 7x + y = -⁴/₃
The system consists of two parallel lines.
