Solve the following system of equations using the substitution method:5x-7y=-18 and 4x+3y=20
from the 2nd:
4x = 20 - 3y
x = 5 - (3/4)y
plug into the 1st:
5x - 7y = -18
5(5 - (3/4)y) - 7y = -18
25 - 15y/4 - 7y = -18
-43y/4 = -43
y = -43(-4/43) = 4
x = 5 - (3/4)4 = 2
(substitution would have been my last choice in the methods to solve this, I would have used elimination)
To solve the system of equations using the substitution method, we need to eliminate one variable by substituting it with an expression involving the other variable.
Let's start by solving one of the equations for one variable in terms of the other. We'll solve the second equation for x:
4x + 3y = 20
Subtract 3y from both sides:
4x = 20 - 3y
Divide by 4:
x = (20 - 3y) / 4
Now that we have x in terms of y, we can substitute this expression into the first equation:
5x - 7y = -18
Instead of writing x, we'll substitute it with (20 - 3y) / 4:
5((20 - 3y) / 4) - 7y = -18
Now simplify and solve for y:
(5(20 - 3y) / 4) - 7y = -18
Multiply both sides by 4 to get rid of fractions:
5(20 - 3y) - 28y = -72
Distribute the 5:
100 - 15y - 28y = -72
Combine like terms:
-43y = -172
Divide by -43:
y = (-172) / (-43)
Simplifying further:
y = 4
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
5x - 7y = -18
Substitute y with 4:
5x - 7(4) = -18
Simplify:
5x - 28 = -18
Add 28 to both sides:
5x = -18 + 28
5x = 10
Divide by 5:
x = 10/5
Simplifying further:
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 4.