Question

use substitution method to solve system
{-5x-3y=-1}
{-4x-2y=0}

Answer 1

To solve the system of equations using the substitution method, we need to solve one of the equations for one variable and substitute it into the other equation.

Let's solve the first equation for x:
-5x - 3y = -1
-5x = 3y - 1
Dividing both sides by -5:
x = (3/5)y + 1/5

Now we substitute this expression for x into the second equation:
-4x - 2y = 0
-4((3/5)y + 1/5) - 2y = 0
-12/5y - 4/5 - 2y = 0
Multiplying through by 5 to eliminate the fractions:
-12y - 4 - 10y = 0
-22y - 4 = 0
-22y = 4
Dividing both sides by -22:
y = -4/22
y = -2/11

Now that we have the value of y, we substitute it back into the first equation to find the value of x:
x = (3/5)(-2/11) + 1/5
x = -6/55 + 11/55
x = 5/55
x = 1/11

Therefore, the solution to the system of equations is x = 1/11 and y = -2/11.