Solve Using a Matrix by Elimination x=7(y-5) , 4y=3x+5

Problem

{[x=7*(y−5)],[4*y=3*x+5])

Solution

1. Rearrange the equations into standard form a*x+b*y=c

x=7*y−35

x−7*y=−35

−3*x+4*y=5

2. Write the system as an augmented matrix.

[[1,−7,|,−35],[−3,4,|,5]]

3. Eliminate the x term in the second row by performing the row operation (R_2)+3*(R_1)⇒(R_2)

3*(1)+(−3)=0

3*(−7)+4=−17

3*(−35)+5=−100

[[1,−7,|,−35],[0,−17,|,−100]]

4. Solve for y using the second row.

−17*y=−100

y=100/17

5. Substitute the value of y back into the first equation to solve for x

x−7*(100/17)=−35

x−700/17=−595/17

x=105/17

Final Answer

(x,y)=(105/17,100/17)

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