Math Question - Solve Equation for Two Unknowns

Solve the following system of equations. If there are no solutions, type "No Solution" for both x and y. If there are infinitely many solutions, type "x" for x, and an expression in terms of x for y.

1x−3y=2
2x−2y=5

x = .
y = .

Comments for Math Question - Solve Equation for Two Unknowns

 Mar 24, 2011 Solve Equation for Two Unknowns by: Staff The question: Solve the following system of equations. If there are no solutions, type "No Solution" for both x and y. If there are infinitely many solutions, type "x" for x, and an expression in terms of x for y. 1x−3y=2 2x−2y=5 x = . y = . The answer: The fastest way to eliminate one of the variables is to add the two equations together. 1x − 3y = 2 2x − 2y = 5 Multiply each side of the first equation by (-2): (-2)*(1x − 3y) = (-2)*(2) 2x − 2y = 5 Eliminate the parentheses in the first equation using the distributive law: (-2)*(1x) − (-2)*(3y) = (-2)*(2) 2x − 2y = 5 -2x + 6y = -4 2x − 2y = 5 Add the two equations. Notice that the variable x is eliminated in the process. This will allow us to solve for the value of y: -2x + 6y = -4 2x − 2y = 5 ----------------- -2x + 2x + 6y - 2y = -4 + 5 0 + 6y - 2y = -4 + 5 6y - 2y = -4 + 5 4y = -4 + 5 4y = 1 Divide each side of the equation by 4: 4y = 1 4y/4 = 1/4 y*(4/4) = 1/4 y*(1) = 1/4 y = 1/4 Since we now know the numerical value of y, we can substitute this value into either of the two original equations, and then solve for x. 1x − 3y = 2 x − 3*(1/4) = 2 x − .75 = 2 add .75 to each side of the equation: x − .75 + .75 = 2 + .75 x + 0 = 2 + .75 x = 2 + .75 x = 2.75 The final answer is: x = 2.75 y = .25 Check the answer by substituting the numerical values of x and y into the original equations: 1x − 3y = 2 2.75 – 3*.25 = 2, correct 2x − 2y = 5 2*2.75 − 2*.25 = 5, correct Since the numerical values of x and y work in both of the original equations, the solutions are correct. Thanks for writing. Staff www.solving-math-problems.com