Solve systems by substitution
5x - 2y = -5
y - 5x = 3
Substitute 5x + 3 for y in the first equation, and solve it for x.
Once you have x, use either of the two equations you wrote to solve for y.
To solve the system of equations by substitution, we will follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
In this case, let's solve the second equation for y in terms of x:
y - 5x = 3
y = 5x + 3
2. Substitute the expression we obtained in step 1 into the other equation.
Substituting 5x + 3 for y in the first equation:
5x - 2(5x + 3) = -5
3. Simplify and solve for x:
5x - 10x - 6 = -5
-5x - 6 = -5
-5x = -5 + 6
-5x = 1
x = 1 / -5
x = -1/5 (or -0.2 as a decimal)
4. Substitute the value of x back into either of the original equations to find y.
Let's use the second equation (y - 5x = 3):
y - 5(-1/5) = 3
y - (-1) = 3
y + 1 = 3
y = 3 - 1
y = 2
Therefore, the solution to the system of equations is:
x = -1/5, y = 2