Explanation:
The system of linear equations can be solved using elimination method or substitution method.
Here's the solution using elimination method:
Add the two equations to eliminate the y variable:
(7y + 10x - 8) + (2y - 5x - 18) = 0 + 0
9y + 5x - 26 = 0
Solve for y:
9y = 26 - 5x
y = (26 - 5x) / 9
Substitute this expression back into either of the original equations to solve for x:
7y + 10x - 8 = 0
7((26 - 5x) / 9) + 10x - 8 = 0
26 - 5x + 70x - 56 = 0
65x - 32 = 0
Solve for x:
65x = 32
x = 32/65
Finally, substitute the value of x back into the expression for y to find the value of y:
y = (26 - 5x) / 9
y = (26 - 5(32/65)) / 9
y = (26 - 160/65) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = 18/9 - 8/3
y = (18 - 24) / 9
y = -6/9
The solution to the system of linear equations is:
x = 32/65
y = -6/9