Question 66534
Well, I hope we can relieve some your confusion and stress!
Solve the system of equations:
{{{x+2y = 6}}} Rewrite this as: {{{x = -2y+6}}} and substitute for x in the second equation.
{{{5x+3y = 2}}}
{{{5(-2y+6)+3y = 2}}} Simplify and solve for y.
{{{-10y+30+3y = 2}}} Combine like-terms.
{{{-7y+30 = 2}}} Subtract 30 from both sides.
{{{-7y = -28}}} Finally, divide by -7.
{{{y = 4}}} Now substitute this for y in the first rewritten equation and solve for x:
{{{x = -2(4)+6}}}
{{{x = -8+6}}}
{{{x = -2}}}
So the solution is: (-2, 4)
The graph of these two lines is shown below, and the point at which the lines intersect is called the solution.
{{{graph(300,200,-5,5,-5,6,(-1/2)x+3,(-5/3)x+(2/3))}}}