Solve each system by substitution:
Solve each system by elimination:
I. Solve each system by substitution:
The method of substitution requires: 1. solving one of the equations in the system for a variable; 2. the next step is to substitute this solution in the other equation in place of that variable. Solve for the remaining variable and perform a check.
Let's perform step 1:
4x + 5y = 7
4x + 5y - 5y = 7 - 5y
4x = 7 - 5y
4x/4 = (7 - 5y)/4
x = 7/4 - 5/4 y
Substitute 7/4 - 5/4 y for x in 9y = 31 + 2x:
9y = 31 + 2(7/4 - 5/4 y)
9y = 31 + 7/2 - 5/2 y
9y = 69/2 - ...
This solution provides a step-by-step explanation of how to solve the given algebra problems.