Solve by Substitution -6x+28y-61=0 , 8x+30y-29=0

Problem

{[−6*x+28*y−61=0],[8*x+30*y−29=0])

Solution

1. Solve the first equation for x by isolating the term −6*x

−6*x=−28*y+61

x=(−28*y+61)/(−6)

x=14/3*y−61/6

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

8*(14/3*y−61/6)+30*y−29=0

3. Distribute the constant 8 through the parentheses.

112/3*y−244/3+30*y−29=0

4. Combine like terms by finding a common denominator for the y terms and the constants.

112/3*y+90/3*y−244/3−87/3=0

202/3*y−331/3=0

5. Solve for y by moving the constant to the right side and multiplying by the reciprocal.

202/3*y=331/3

y=331/202

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

x=14/3*(331/202)−61/6

x=(7⋅331)/(3⋅101)−61/6

x=2317/303−61/6

7. Simplify the fraction for x using a common denominator of 606

x=4634/606−6161/606

x=−1527/606

x=−509/202

Final Answer

(x,y)=(−509/202,331/202)

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