Solve by Substitution 5x+3y=-7 , 7x-3y=55

Problem

{[5*x+3*y=−7],[7*x−3*y=55])

Solution

1. Isolate one variable in the first equation. We will solve for 3*y to make the substitution into the second equation easier.

5*x+3*y=−7

3*y=−7−5*x

2. Substitute the expression for 3*y into the second equation. Note that the second equation contains −3*y which is the negative of our isolated expression.

7*x−(3*y)=55

7*x−(−7−5*x)=55

3. Solve for x by distributing the negative sign and combining like terms.

7*x+7+5*x=55

12*x+7=55

12*x=48

x=4

4. Substitute the value of x back into the isolated expression for 3*y to find y

3*y=−7−5*(4)

3*y=−7−20

3*y=−27

y=−9

Final Answer

(x,y)=(4,−9)

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