Find the solution of the system of equations.
minus, 5, x, plus, 7, y, equals, 40
−5x+7y=
40
10, x, plus, 7, y, equals, 25
10x+7y=
25
To solve the system of equations, we can use the method of substitution.
From the first equation, we have -5x + 7y = 40.
To isolate one variable, we can solve this equation for x in terms of y:
-5x = 40 - 7y
x = (40 - 7y)/(-5)
x = (7y - 40)/5
Now we can substitute this expression for x into the second equation:
10((7y - 40)/5) + 7y = 25
Multiply both sides by 5 to get rid of the fraction:
10(7y - 40) + 35y = 125
Distribute the 10:
70y - 400 + 35y = 125
Combine like terms:
105y - 400 = 125
Add 400 to both sides:
105y = 525
Divide both sides by 105:
y = 5
Now that we have the value of y, we can substitute it back into either of the original equations to solve for x.
Using the first equation:
-5x + 7(5) = 40
-5x + 35 = 40
Subtract 35 from both sides:
-5x = 5
Divide both sides by -5:
x = -1
So the solution to the system of equations is x = -1, y = 5.