Identify the solution(s) of the system of equations, if any.
x + 2y = 7
3x - 6y = 3
(4, )
(4, )
(, 4)
(, 4)
Eq1: x + 2y = 7
Eq2: 3x - 6y = 3
Multiply Eq1 by -3 and add the Eqs:
-3x - 6y = -21
+3x - 6y = 3
Sum: -12y = -18
Y = -18/-12 = 3/2
In Eq1, replace Y with 3/2 and solve for X:
x + 2*3/2 = 7
X = 7-3 = 4.
Solution: (4, 3/2).
To identify the solution(s) of the system of equations, we can use the method of substitution or elimination.
Let's first use the method of substitution:
1. Solve the first equation for x:
x = 7 - 2y
2. Substitute the value of x into the second equation:
3(7 - 2y) - 6y = 3
3. Simplify and solve for y:
21 - 6y - 6y = 3
-12y = -18
y = -18 / -12
y = 3/2 = 1.5
4. Substitute the value of y back into the first equation to find x:
x + 2(1.5) = 7
x + 3 = 7
x = 7 - 3
x = 4
Therefore, the solution to the system of equations is (4, 1.5).