Solve Using a Matrix by Elimination y=4x+3x-2 , y=6

Problem

{[y=4*x+3*x−2],[y=6])

Solution

1. Simplify the first equation by combining the like terms 4*x and 3*x to get 7*x

y=7*x−2

2. Rearrange the equations into standard form A*x+B*y=C to prepare for the augmented matrix.

−7*x+y=−2

0*x+y=6

3. Write the system as an augmented matrix.

[[−7,1,|,−2],[0,1,|,6]]

4. Perform row operations to eliminate the y term in the first row. Subtract the second row ((R_2) from the first row ((R_1).

(R_1)−(R_2)⇒(R_1)

[[−7,0,|,−8],[0,1,|,6]]

5. Divide the first row by −7 to solve for x

−1/7*(R_1)⇒(R_1)

[[1,0,|,8/7],[0,1,|,6]]

6. Identify the values of x and y from the resulting identity matrix.

x=8/7

y=6

Final Answer

(x,y)=(8/7,6)

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