Question 332786
Solve:
1) {{{x/5 + 3y = 31}}}
2) {{{2x-y/5 = 8}}} First multiply both sides of both equations by 5 to clear the fractons.
1a) {{{5(x/5 + 3y) = 5(31)}}}
1b) {{{x+15y = 155}}}
2a) {{{5(2x-y/5) = 5(8)}}}
2b) {{{10x-y = 40}}}
Now you have a choice here.  You want to get both equations to have the number of either the x-variable or the y-variable so that you can subtract (or add) the two equation to eliminate that variable.  I chose to multiply equation 1b) by 10 so that I can eliminate the x-variable by subtracting.
1c) {{{10x+150y = 1550}}}
2b) {{{10x-y = 40}}} Subtract equation 2b) from equation 1c) which eliminates the x-variable.
3) {{{151y = 1510}}} Now divide both sides by 151.
3a) {{{highlight(y = 10)}}} Now substitute this into equation 1) or 2) to solve for x.  I chose equation 2).
{{{2x-y/5 = 8}}} Substitute y = 10.
{{{2x-10/5 = 8}}} Simplify.
{{{2x-2 = 8}}} Add 2 to both sides.
{{{2x = 10}}} Divide both sides by 2.
{{{highlight(x = 5)}}}
The answer is: (5, 10)