Mathematics
yani123
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How to solve systems of equations: 4x+5y=11                                                      2x+6y=16          show steps plz

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(2) Answers
maria169

4x+5y=11 2x+6y=16 2x=16-6y x=8-3y 4(8-3y)+5y=11 32-12y+5y=11 -7y=-21 y=3 4x+5(3)=11 4x+15=11 4x=-4 x=-1 (-1,3)

Mirulll

4x+5y = 11 and 2x+6y = 16 Let's start by solving 4x+5y = 11 for the variable x. Move the 5y to the right hand side by subtracting 5y from both sides, like this: From the left hand side: 5y - 5y = 0 The answer is 4x From the right hand side: The answer is 11-5y Now, the equation reads: 4x = 11-5y  To isolate the x, we have to divide both sides of the equation by theother variables around the x on the left side of the equation. The last step is to divide both sides of the equation by 4 like this: To divide x by 1 The x just gets copied along in the numerator.The answer is x4x ÷ 4 = x To divide 11-5y by 4divide each term in 11-5y by 4 term by term.11 ÷ 4 =11/4 To divide y by 1 The y just gets copied along in the numerator.-5y ÷ 4 =The solution to your equation is: x =Next, let's solve 2x+6y = 16 for the variable y. Move the 2x to the right hand side by subtracting 2x from both sides, like this: From the left hand side: 2x - 2x = 0The answer is 6yFrom the right hand side: The answer is 16-2x Now, the equation reads: 6y = 16-2x  To isolate the y, we have to divide both sides of the equation by theother variables around the y on the left side of the equation. The last step is to divide both sides of the equation by 6 like this: To divide y by 1The y just gets copied along in the numerator.The answer is y6y ÷ 6 = yTo divide 16-2x by 6divide each term in 16-2x by 6 term by term.16 ÷ 6 =To divide x by 1The x just gets copied along in the numerator.-2x ÷ 6 =The solution to your equation is: y =Now, plug the earlier result, x=11/4-5/4y, in for x everywhere it occurs in  y=8/3-1/3x. This gives 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 to 1/3 evaluates to 11/4 evaluates to 5/4 evaluates to Multiply y andMultiply y and 1The y just gets copied along.The answer is yy5/4*y evaluates to 11/4-5/4*y evaluates to Multiply bywe multiply by each term in term by term.This is the distributive property of multiplication.Multiply and1 × =Multiply andMultiply 1 and yThe y just gets copied along.y × =1/3*(11/4-5/4*y) evaluates to  - =The answer is8/3-1/3*(11/4-5/4*y) evaluates to Move the to the left hand side by subtracting from both sides, like this: From the left hand side: y - =The answer isFrom the right hand side:  - = 0The answer is Now, the equation reads:  =  To isolate the y, we have to divide both sides of the equation by theother variables around the y on the left side of the equation. The last step is to divide both sides of the equation by like this: To divide y by 1The y just gets copied along in the numerator.The answer is y ÷ = y ÷ = 3The solution to your equation is: y = 3Lastly, to find the solution for x, we plug this answer for y into the earlier result that x=11/4-5/4y. This gives x=11/4-5/4(3). Now, simplify this. 11/4 evaluates to 5/4 evaluates to Multiply and 315/4*(3) evaluates to 11/4-5/4*(3) evaluates to -1x= -1So, the solutions to your equations are: x= -1 and y= 3The answer is xThe answer is y

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