Question 744227
Call 7x + 5y = 77 equation I, and called 3x - 4y = -10 equation II.
Then from equation I, if you -5y from both sides of the equation:
{{{7x = 77 - 5y}}} ,
Then dividing both sides by 7:
{{{x = 11 - (5/7)y}}} .

We can then substitute this expression for x into equation II. This gives us:

{{{3(11 - (5/7)y) - 4y = -10}}} .

Expanding the brackets:

{{{33 - (15/7)y - 4y = -10}}}, which is equivalent to,

{{{43 = (43/7)y}}}, which gives us that

{{{y = 7}}}.

Then substituting this back into our expression for x gives us:
{{{x = 11 - (5/7)*7}}}, 
which give us that 
{{{x = 6}}}

Best to check these answers by substituting them back into the original equations.