solve with substitution
5x - y=-1
15x=2y
solve the first equation for y.
5x-y=-1 subtract 5x from both sides
-y=-1-5x divide by -1
y=1+5x
now, plug this answer in for y in the second equation.
15x=2y
15x=2(1+5x)
15x=2+10x
5x=2
x=.4
plug this(x=.4) into the equation for y.
y=1+5x
y=1+5(.4)
y=1+2
y=2
therefore, x=.4 and y=2 or (.4, 2)
actually that does not work out, plug x and y into original equation...
actually that does not work out, plug x and y into original equation...
y=1+2
y=3
then it works out
To solve this system of equations using substitution, we can follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
15x = 2y
Divide both sides by 2:
7.5x = y
Step 2: Substitute the expression we found for y into the other equation.
Replace y in the first equation with 7.5x:
5x - (7.5x) = -1
Step 3: Solve the resulting equation for x.
Combine like terms:
-2.5x = -1
Divide both sides by -2.5:
x = 0.4
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's substitute x = 0.4 into the first equation:
5(0.4) - y = -1
2 - y = -1
Subtract 2 from both sides:
- y = -3
Multiply both sides by -1:
y = 3
So the solution to the system of equations is x = 0.4 and y = 3.