Question 1053541
Algebra of each step



Step 1: {{{(2/3)x + 2y = 8}}}



Step 2: {{{(2/3)x + 2y-(2/3)x = 8-(2/3)x}}}



Step 3: {{{2y = -(2/3)x+8}}}



Step 4: {{{(1/2)*2y = (1/2)*(-(2/3)x+8)}}}



Step 5: {{{y = (1/2)*(-(2/3)x)+(1/2)*(8)}}}



Step 6: {{{y = (-1/3)x+(1/2)*(8)}}}



Step 7: {{{y = (-1/3)x+4}}}



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Explanation of the steps above



Step 1: Original equation (No work done so far)



Step 2: Subtract {{{(2/3)x}}} from both sides



Step 3: Combine like terms on the left side. Notice how the x terms on the left side combine to 0x = 0 and they effectively go away. On the right side, I simply flipped the terms.



Step 4: Multiply both sides by {{{1/2}}} to isolate y. Note: {{{(1/2)*(2) = 2/2 = 1}}}



Step 5: Distribute



Step 6: Multiply {{{1/2}}} with {{{-(2/3)x}}} to get {{{(1/2)*(-(2/3)x) = (1/2)*(-2/3)x = ((1*(-2))/(2*3))x = (-2/6)x = (-1/3)x}}}



Step 7: Multiply {{{1/2}}} with {{{8}}} to get {{{(1/2)*8 = (1/2)*(8/1) = (1*8)/(2*1) = 8/2 = 4}}}



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After those 7 steps, the equation {{{(2/3)x + 2y = 8}}} turns into {{{y = (-1/3)x+4}}}



The final answer is {{{y = (-1/3)x+4}}}



In this case, the equation is in the form {{{y = mx+b}}} where the slope is {{{m = -1/3}}} and the y intercept is {{{b = 4}}}