Question 1093252
You must show all of your work to receive credit. All or nothing. Solve the system using any method. 3/x+4/y=5/2.     6/x+1/y=1/2
<pre>{{{3/x + 4/y = 5/2	}}} ------ eq (i)
{{{6/x + 1/y = 1/2}}} ------ eq (ii)	
{{{- 6/x - 8/y = - 10/2}}} ------ Multiplying eq (i) by - 2 ------ eq (iii)	
{{{- 7/y = - 9/2}}} ---------- Adding eqs (iii) & (ii)	
- 9y = - 14 -------- Cross-multiplying
{{{highlight_green(matrix(1,7, y, "=", (- 14)/(- 9), "=", 14/9, or, 1&5/9))}}}

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Instead of substituting the value of y into one of the equations, it's best to repeat the process, as follows:
{{{3/x + 4/y = 5/2	}}} ------ eq (i)
{{{6/x + 1/y = 1/2}}} ------ eq (ii)	
{{{- 24/x - 4/y = - 4/2}}} ------ Multiplying eq (ii) by - 4 ------ eq (iii)	
{{{- 21/x = 1/2}}} ---------- Adding eqs (iii) & (i)	
x = - 21(2) ------- Cross-multiplying
{{{highlight_green(matrix(1,3, x, "=", - 42))}}}</pre>