Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y + 4x = 18 2y – 3x = 4 A. (6, –3) B. (5, –1) C. (2, 5) D. (3, 3)
Mathematics · High School · Thu Feb 04 2021
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Given the equation:
2y + 4x = 18
2y - 3x = 4
Solve for the systems of equation.
Solution:
In order to solve for the systems of equation, we must first solve for the value of y of the 2nd equation, and substitute it to the 1st equation.
2y - 3x = 4
Transpose -3x to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
2y = 3x + 4
Divide both sides by 2 in order to determine the value of y.
2y/2 = (3x + 4)/2
y = 3/2x + 2
Substitute the value of y to the first equation:
2 (3/2x + 2) + 4x = 18
3x + 2 + 4x = 18
7x + 2 = 18
Transpose 2 to the other side of the equation.
7x = 18 - 2
7x = 16
Divide both sides by 7 in order to determine the value of x.
x = 16/7
x = 2.3
Substitute the value of x to the equation of y.
y = (3/2)(16/7) + 2
y = 48/14 + 2
y = 3.42 + 2
y = 5.4
Final answer:
(2.3, 5.4)