Question 515386
Since the second equation is already solved for x, we can substitute its right hand side for x in the first equation and get a new equation involving only y:

{{{5x + 2y = 4}}}
{{{ 5(61 - 9y) + 2y = 4}}} (substituting 61 - 9y for x)

Now we solve for y:

{{{ 305 - 45y + 2y = 4}}} (distributing 5 on the left side)
{{{ 305 - 43y = 4}}} (combining like terms)
{{{ -43y = -301}}} (subtracting 305 from both sides)
{{{ y = 7 }}} (divide both sides by -43)

So y = 7.  To get x, we now substitute 7 for x in the first equation:

{{{ x = 61 - 9y = 61 - 9(7) = 61 - 63 = -2}}}

SO our solution is x = -2 and y = 7.  Let's check this.  For the first equation, we get

{{{5x + 2y = 5(-2) + 2(7) = -10 + 14 = 4}}}

so that works.  For the second equation, we get:

{{{ x = 61 - 9y}}}
{{{-2 = 61 - 9(7)}}}
{{{ -2 = 61 - 63}}}

which also works.  So x = -2 and y = 7 is the correct solution.