Identify the solution(s) of the system of equations, if any.
3x + 2y = 4
5x - 4y = 3
a) (1, 0.5)
b) (0, 5.1)
c) (5,5.5)
d) (5/11, -2/11)
well you can always just plug the answers into both equations and solve them.
Answer: A
Identify the solution(s) of the system of equations, if any.
-4x - 4y = 4
4y = -4x - 4
A) no solution
B) (0, -1)
C) (-1, 0)
D) infinitely many solutions
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.
First, let's eliminate one of the variables by multiplying the equations by suitable constants so that the coefficients of one of the variables will be the same, but with opposite signs.
Let's eliminate the x term. Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x equal:
5(3x + 2y) = 5(4)
3(5x - 4y) = 3(3)
15x + 10y = 20
15x - 12y = 9
Next, subtract the second equation from the first equation to eliminate the x term:
(15x + 10y) - (15x - 12y) = 20 - 9
15x + 10y - 15x + 12y = 11
22y = 11
Now, solve for y by dividing both sides of the equation by 22:
22y/22 = 11/22
y = 0.5
Substitute this value of y back into either of the original equations to solve for x. Let's use the first equation:
3x + 2(0.5) = 4
3x + 1 = 4
3x = 4 - 1
3x = 3
x = 1
Therefore, the solution to the system of equations is (1, 0.5).
So, the correct option is a) (1, 0.5).