eq1 y = 2x + 3
eq2 y = 1x + 2
What is the solution for eq1 and eq 2? Remember we are looking for the "common" x and y pairs that solve BOTH equations.
Are any of the following (x,y) pairs a solution to the above systems of equations? (2, 4) ? (-1, 1) ? Why?
set y = y
2x+3 = x+2
x = -1
sub back into either original equation
y = x+2 ---> y = -1+2 = 1
so x=-1, y = 1 is the solution
sub those values back into both equations, they work for both
(2,4) works in the 2nd but not the 1st.
To find the solution for the system of equations, we need to determine the values of x and y that satisfy both equations simultaneously. In other words, we are looking for the values of x and y that make both eq1 and eq2 true.
To determine if a given (x, y) pair is a solution to the system, we can substitute the values into the equations and see if both equations yield true statements.
Let's test each pair of values:
1. (2, 4):
Substituting x = 2 and y = 4 into eq1:
4 = 2(2) + 3
4 = 4 + 3
4 = 7 (This is not true)
Substituting x = 2 and y = 4 into eq2:
4 = 1(2) + 2
4 = 2 + 2
4 = 4 (This is true)
Since both equations do not yield true statements when (x, y) = (2, 4), this pair of values is not a solution to the system.
2. (-1, 1):
Substituting x = -1 and y = 1 into eq1:
1 = 2(-1) + 3
1 = -2 + 3
1 = 1 (This is true)
Substituting x = -1 and y = 1 into eq2:
1 = 1(-1) + 2
1 = -1 + 2
1 = 1 (This is true)
Since both equations yield true statements when (x, y) = (-1, 1), this pair of values is a solution to the system.
Therefore, the (x, y) pair (-1, 1) is a solution to the system of equations, while (2, 4) is not a solution.