what would be the ordered pairs for the linear equations 3x +4y = 18 and x + 3y =11
3x+4y=18 multipy the second equation by 3 then
3x+9y=33
subtract the second equation from the first...
-5y=-15
solve for y, then put that value for y into either equation, solve for x.
To find the ordered pairs for the linear equations 3x + 4y = 18 and x + 3y = 11, we can solve the system of equations using the method of substitution or elimination.
Let's start with the method of substitution:
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation (x + 3y = 11) for x:
x = 11 - 3y
2. Substitute the expression for x obtained in step 1 into the other equation (3x + 4y = 18):
3(11 - 3y) + 4y = 18
Simplify the equation:
33 - 9y + 4y = 18
-5y = -15
y = 3
3. Substitute the value of y obtained in step 2 into the expression for x (x = 11 - 3y):
x = 11 - 3(3)
x = 11 - 9
x = 2
Therefore, the ordered pair (x, y) for the first equation is (2, 3).
To find the second ordered pair, we can solve the second equation (x + 3y = 11) for x:
1. Solve the second equation (x + 3y = 11) for x:
x = 11 - 3y
2. Substitute the expression for x obtained in step 1 into the first equation (3x + 4y = 18):
3(11 - 3y) + 4y = 18
Simplify the equation:
33 - 9y + 4y = 18
-5y = -15
y = 3
3. Substitute the value of y obtained in step 2 into the expression for x (x = 11 - 3y):
x = 11 - 3(3)
x = 11 - 9
x = 2
Therefore, the ordered pair (x, y) for the second equation is also (2, 3).
Hence, the ordered pairs for the system of equations 3x + 4y = 18 and x + 3y = 11 are (2, 3), and (2, 3).