# How to solve systems of equations: 4x+5y=11Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2x+6y=16 Â Â Â Â Â show steps plz

###### Question:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2x+6y=16 Â Â Â Â Â show steps plz

## Answers

4x+5yÂ =Â 11Â andÂ 2x+6yÂ =Â 16Let's start by solvingÂ 4x+5yÂ =Â 11Â for the variable x.Move theÂ 5yÂ to the right hand side by subtractingÂ 5yÂ from both sides, like this:From the left hand side:5yÂ -Â 5yÂ =Â 0The answer isÂ 4xFrom the right hand side:The answer isÂ 11-5yNow, the equation reads:4xÂ =Â 11-5yÂ To isolate the x, we have to divide both sides of the equation by theotherÂ variablesaround the x on the left side of the equation.The last step is to divide both sides of the equation byÂ 4Â like this:To divideÂ xÂ byÂ 1TheÂ xÂ just gets copied along in the numerator.The answer isÂ x4xÂ Ã·Â 4Â =Â xTo divideÂ 11-5yÂ byÂ 4divide each term inÂ 11-5yÂ byÂ 4Â term by term.11Â Ã·Â 4Â =11/4To divideÂ yÂ byÂ 1TheÂ yÂ just gets copied along in the numerator.-5yÂ Ã·Â 4Â =The solution to your equation is:xÂ =Next, let's solveÂ 2x+6yÂ =Â 16Â for the variable y.Move theÂ 2xÂ to the right hand side by subtractingÂ 2xÂ from both sides, like this:From the left hand side:2xÂ -Â 2xÂ =Â 0The answer isÂ 6yFrom the right hand side:The answer isÂ 16-2xNow, the equation reads:6yÂ =Â 16-2xÂ To isolate the y, we have to divide both sides of the equation by theotherÂ variablesaround the y on the left side of the equation.The last step is to divide both sides of the equation byÂ 6Â like this:To divideÂ yÂ byÂ 1TheÂ yÂ just gets copied along in the numerator.The answer isÂ y6yÂ Ã·Â 6Â =Â yTo divideÂ 16-2xÂ byÂ 6divide each term inÂ 16-2xÂ byÂ 6Â term by term.16Â Ã·Â 6Â =To divideÂ xÂ byÂ 1TheÂ xÂ just gets copied along in the numerator.-2xÂ Ã·Â 6Â =The solution to your equation is:yÂ =Now, plug the earlier result,Â x=11/4-5/4y, in for x everywhere it occurs inÂ y=8/3-1/3x.This givesÂ y=8/3-1/3(11/4-5/4y). Now all we have to do is solve this for y,to have our first solution.8/3 evaluates toÂ 1/3 evaluates toÂ 11/4 evaluates toÂ 5/4 evaluates toÂ MultiplyÂ yÂ andMultiplyÂ yÂ andÂ 1TheÂ yÂ just gets copied along.The answer isÂ yy5/4*y evaluates toÂ 11/4-5/4*y evaluates toÂ MultiplyÂ bywe multiplyÂ by each term inÂ term by term.This is the distributive property of multiplication.MultiplyÂ and1Â Ã—Â =MultiplyÂ andMultiplyÂ 1Â andÂ yTheÂ yÂ just gets copied along.yÂ Ã—Â =1/3*(11/4-5/4*y) evaluates toÂ Â -Â =The answer is8/3-1/3*(11/4-5/4*y) evaluates toÂ Move theÂ to the left hand side by subtractingÂ from both sides, like this:From the left hand side:yÂ -Â =The answer isFrom the right hand side:Â -Â =Â 0The answer isNow, the equation reads:Â =Â To isolate the y, we have to divide both sides of the equation by theotherÂ variablesaround the y on the left side of the equation.The last step is to divide both sides of the equation byÂ like this:To divideÂ yÂ byÂ 1TheÂ yÂ just gets copied along in the numerator.The answer isÂ yÂ Ã·Â =Â yÂ Ã·Â =Â 3The solution to your equation is:yÂ =Â 3Lastly, to find the solution for x, we plug this answer for y into the earlier result thatx=11/4-5/4y.This givesÂ x=11/4-5/4(3). Now, simplify this.11/4 evaluates toÂ 5/4 evaluates toÂ MultiplyÂ andÂ 315/4*(3) evaluates toÂ 11/4-5/4*(3) evaluates toÂ -1x=Â -1So, the solutions to your equations are:x=Â -1Â and y=Â 3The answer isÂ xThe answer isÂ y

4x+5y=112x+6y=16 2x=16-6yx=8-3y4(8-3y)+5y=1132-12y+5y=11-7y=-21y=3 4x+5(3)=114x+15=114x=-4x=-1 (-1,3)