Solve by Substitution 3x+4y=97 , 2x+3y=69

Problem

{[3*x+4*y=97],[2*x+3*y=69])

Solution

1. Isolate the variable x in the second equation by subtracting 3*y from both sides and dividing by 2

2*x=69−3*y

x=(69−3*y)/2

2. Substitute the expression for x into the first equation.

3*((69−3*y)/2)+4*y=97

3. Eliminate the fraction by multiplying the entire equation by 2

3*(69−3*y)+8*y=194

4. Distribute the 3 and combine the y terms.

207−9*y+8*y=194

207−y=194

5. Solve for y by subtracting 207 from both sides and multiplying by −1

−y=−13

y=13

6. Substitute the value of y back into the expression for x to find the final value.

x=(69−3*(13))/2

x=(69−39)/2

x=30/2

x=15

Final Answer

(x,y)=(15,13)

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