5x + 3y = 2
10x + 7y = 5
Use the substitution method. Solve for x in the first equation.
5x + 3y = 2
Subtract 3y from both sides.
5x = 2 - 3y
Divide both sides by 5.
x = 2/5 - 3/5y
Now plug in x into the second equation, 10x + 7y = 5.
10(2/5 - 3/5y) + 7y = 5
Multiply (2/5 - 3/5y) by 10.
4 - 6y + 7y = 5
Combine like terms.
4 + y = 5
Subtract 4 from both sides.
y = 1
Now plug y back into the first equation, 5x + 3y = 2.
5x + 3(1) = 2
5x + 3 = 2
Subtract 3 from both sides.
5x = -1
Divide both sides by 5.
x = -1/5
y = 1