Identify the solution of the system of equations
-3x-4y=2
8y=6x-4
(0,-1/2)
Identify the solution of the system of equations
3x+2y=4
5x-4y=3
(1,1/2)
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Identify the solution(s) of the system of equations, if any. -3x - 4y =2 8y = - 6x - 4
To find the solution of a system of equations, we need to solve both equations simultaneously. We can use the method of substitution or elimination to find the values of x and y that satisfy both equations.
Let's solve the system of equations using the substitution method:
1) Start with the equation -3x - 4y = 2.
2) Solve this equation for x in terms of y:
-3x = 2 + 4y
Divide both sides by -3:
x = (-2/3) - (4/3)y
3) Substitute the expression for x in the second equation:
8y = 6((-2/3) - (4/3)y) - 4
4) Simplify and solve for y:
8y = -4 - 8y - 4
Move the like terms to one side:
16y = -8
Divide both sides by 16:
y = -1/2
5) Substitute the value of y back into either of the original equations to solve for x:
-3x - 4(-1/2) = 2
-3x + 2 = 2
-3x = 0
x = 0
Therefore, the solution to the system of equations is x = 0, y = -1/2.