Solve by Substitution 4x+7y=15 , 6x-5y=21

Problem

{[4*x+7*y=15],[6*x−5*y=21])

Solution

1. Isolate the variable x in the first equation by subtracting 7*y from both sides and dividing by 4

4*x=15−7*y

x=(15−7*y)/4

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

6*((15−7*y)/4)−5*y=21

3. Simplify the equation by distributing the 6 and multiplying the entire equation by 2 to clear the denominator.

(3*(15−7*y))/2−5*y=21

3*(15−7*y)−10*y=42

45−21*y−10*y=42

4. Solve for y by combining like terms and isolating the variable.

45−31*y=42

−31*y=−3

y=3/31

5. Substitute the value of y back into the expression for x to find the value of the second variable.

x=(15−7*(3/31))/4

x=(465/31−21/31)/4

x=444/31/4

x=111/31

Final Answer

(x,y)=(111/31,3/31)

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