How do you solve the following linear system: ${(4x + 5y = -3) ,( y = 1/2x - 3/2):}$ ?

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Answer 1 · 2018-03-13T21:20:12

See explanation.

You can solve the equation by replacing $y$ in the first equation with $1/2x-3/2$ from the second equation:

${(4x+5(1/2x-3/2)=-3),(y=1/2x-3/2):}$

${(4x+5/2x-15/2=-3),(y=1/2x-3/2):}$

Now we can calculate $x$ from the first equation:

${(13/2x=-3+15/2),(y=1/2x-3/2):}$

${(13/2x=9/2),(y=1/2x-3/2):}$

${(13x=9),(y=1/2x-3/2):}$

${(x=9/13),(y=9/26-3/2):}$

Last step is to put the calculated value of $x$ into the second equation to calculate $y$ :

${(x=9/13),(y=9/26-39/26):}$

${(x=9/13),(y=-1 2/13):}$

How do you solve the following linear system: {(4x + 5y = -3) ,( y = 1/2x - 3/2):} {(4x + 5y = -3) ,( y = 1/2x - 3/2):} ?