How many solutions does this linear system have? Y=2/3x+2 6x-4y=-10
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Given the equation:
y = ⅔x + 2
6x - 4y = -10
Determine the solutions in the linear equation.
Solution:
In order to determine the solutions in the linear equation, we simply need to substitute the value of y from the first equation to the the second equation, and then solve for x.
6x - 4(⅔x) + 2 = -10
6x - 8/3x + 2 =-10
6x can be written as, 18/3 in order to easily compute the equation.
18/3x - 8/3x + 2 = -10
10/3x + 2= -10
Transpose 2 on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
10/3x = -10 - 2
10/3x = -12
Multiply both sides by 3/10 in order to cancel out 10/3x, leaving behind x.
(3/10)(10/3x) = (3/10)(-12)
x = -36/10 or 3.6
Final answer:
x = -36/10 or 3.6