this is a practice question, not a quiz:
How many solutions does the system of equation have?
2x + 3y = 9 and y = 2/3x -2
A.
One solution
B.
Two solutions
C.
Infinitely many solutions
D.
No solutions
since the slopes are different, the two lines must intersect in one point.
Gf tf vg
So one?
To find the number of solutions for the given system of equations, we can use one of the methods of solving systems of equations, such as substitution or elimination.
In this case, we can use the substitution method by substituting the value of y from the second equation into the first equation.
Given equations:
1) 2x + 3y = 9 ----------- (Equation 1)
2) y = 2/3x - 2 ----------- (Equation 2)
Substitute Equation 2 into Equation 1:
2x + 3(2/3x - 2) = 9
Simplify:
2x + 2x - 6 = 9
Combine like terms:
4x - 6 = 9
Add 6 to both sides:
4x = 15
Divide both sides by 4:
x = 15/4 or x = 3.75
Now, substitute the value of x into the second equation to find the value of y:
y = 2/3(3.75) - 2
y = 2.5 - 2
y = 0.5
So, the values of x and y that satisfy both equations are x = 3.75 and y = 0.5.
Since the values for x and y are unique and there is only one combination of values that satisfies both equations, the system of equations has one solution.
Therefore, the answer is A. One solution.