Write an article based on this summary:

Try this problem using the distributive property with one variable: Try this problem involving a fraction: Try solving this system of equations:
5(x+4)=6x−5{\displaystyle 5(x+4)=6x-5}.  Use the distributive property to cancel the parentheses:5(x+4)=6x−5{\displaystyle 5(x+4)=6x-5}5x+20=6x−5{\displaystyle 5x+20=6x-5}  Cancel the 5x{\displaystyle 5x} on the left side of the equation by subtracting 5x{\displaystyle 5x} from both sides:5x+20=6x−5{\displaystyle 5x+20=6x-5}5x+20−5x=6x−5−5x{\displaystyle 5x+20-5x=6x-5-5x}20=x−5{\displaystyle 20=x-5}  Isolate the variable by adding 5 to each side of the equation:20=x−5{\displaystyle 20=x-5}20+5=x−5+5{\displaystyle 20+5=x-5+5}25=x{\displaystyle 25=x} −7+3x=7−x2{\displaystyle -7+3x={\frac {7-x}{2}}}.  Remove the fraction. To do this, multiply each side of the equation by the fraction’s denominator:−7+3x=7−x2{\displaystyle -7+3x={\frac {7-x}{2}}}2(−7+3x)=2(7−x2){\displaystyle 2(-7+3x)=2({\frac {7-x}{2}})}−14+6x=7−x{\displaystyle -14+6x=7-x}  Cancel the −x{\displaystyle -x} on the right side of the equation by adding x{\displaystyle x} to each side of the equation:−14+6x=7−x{\displaystyle -14+6x=7-x}−14+6x+x=7−x+x{\displaystyle -14+6x+x=7-x+x}−14+7x=7{\displaystyle -14+7x=7}  Move the constants to one side of the equation by adding 14 to each side:−14+7x=7{\displaystyle -14+7x=7}−14+7x+14=7+14{\displaystyle -14+7x+14=7+14}7x=21{\displaystyle 7x=21}  Cancel the coefficient by dividing each side of the equation by 7:7x=21{\displaystyle 7x=21}7x7=217{\displaystyle {\frac {7x}{7}}={\frac {21}{7}}}x=3{\displaystyle x=3} 9x+15=12y;9y=9x+27{\displaystyle 9x+15=12y;9y=9x+27}  Isolate the y{\displaystyle y} variable in the second equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(x+3){\displaystyle 9y=9(x+3)}9y9=9(x+3)9{\displaystyle {\frac {9y}{9}}={\frac {9(x+3)}{9}}}y=x+3{\displaystyle y=x+3}  Plug in x+3{\displaystyle x+3} for y{\displaystyle y} in the first equation:9x+15=12y{\displaystyle 9x+15=12y}9x+15=12(x+3){\displaystyle 9x+15=12(x+3)}  Use the distributive property to cancel the parentheses:9x+15=12x+36{\displaystyle 9x+15=12x+36}  Cancel the variable on the left side of the equation by subtracting 9x{\displaystyle 9x} from each side:9x+15=12x+36{\displaystyle 9x+15=12x+36}9x+15−9x=12x+36−9x{\displaystyle 9x+15-9x=12x+36-9x}15=3x+36{\displaystyle 15=3x+36}  Move the constants to one side by subtracting 36 from each side:15=3x+36{\displaystyle 15=3x+36}15−36=3x+36−36{\displaystyle 15-36=3x+36-36}−21=3x{\displaystyle -21=3x}  Cancel the coefficient by dividing each side by 3:−21=3x{\displaystyle -21=3x}−213=3x3{\displaystyle {\frac {-21}{3}}={\frac {3x}{3}}}−7=x{\displaystyle -7=x}  Solve for y{\displaystyle y} by plugging the value of x{\displaystyle x} into either equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(−7)+27{\displaystyle 9y=9(-7)+27}9y=−63+27{\displaystyle 9y=-63+27}9y=−36{\displaystyle 9y=-36}9y9=−369{\displaystyle {\frac {9y}{9}}={\frac {-36}{9}}}y=−4{\displaystyle y=-4}