Solve by Addition/Elimination 3x-4y=4 , x+3y=-3

Problem

{[3*x−4*y=4],[x+3*y=−3])

Solution

1. Identify the system of equations and choose a variable to eliminate. We will eliminate x by multiplying the second equation by −3

x+3*y=−3⇒−3*(x+3*y)=−3*(−3)

−3*x−9*y=9

2. Add the modified second equation to the first equation to eliminate the x terms.

(3*x−4*y)+(−3*x−9*y)=4+9

−13*y=13

3. Solve for y by dividing both sides by −13

y=−1

4. Substitute the value of y back into the original second equation to find x

x+3*(−1)=−3

x−3=−3

5. Solve for x by adding 3 to both sides.

x=0

Final Answer

(x,y)=(0,−1)

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