0.3x + 0.2y=5, 0.5x + 0.4y=11 using the substitution method
.3x + .2y = 5
so
3x + 2y = 50
y = 25 - 3x/2
.5x + .4y = 11
5x + 4y = 110
5x + 4(25 - 3x/2) = 110
5x + 100 - 6x = 110
-x = 10
x = -10
y = 40
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation (0.3x + 0.2y = 5) for x:
0.3x + 0.2y = 5
0.3x = 5 - 0.2y
x = (5 - 0.2y) / 0.3
Step 2: Substitute the expression obtained in step 1 into the other equation.
Now, substitute the value of x from the first equation into the second equation (0.5x + 0.4y = 11):
0.5[(5 - 0.2y) / 0.3] + 0.4y = 11
Step 3: Simplify and solve the equation for y.
Multiply the numerator (5 - 0.2y) of the fraction by 0.5, then divide by 0.3:
(2.5 - 0.1y) / 0.3 + 0.4y = 11
(2.5 - 0.1y)/0.3 + 0.4y = 11
Step 4: Solve the equation for y.
Multiply both sides of the equation by 0.3 to eliminate the denominator:
2.5 - 0.1y + 0.12y = 11 * 0.3
2.5 + 0.02y = 3.3
Subtract 2.5 from both sides:
0.02y = 3.3 - 2.5
0.02y = 0.8
Divide both sides by 0.02 to solve for y:
y = 0.8 / 0.02
y = 40
Step 5: Substitute the value of y into one of the original equations and solve for x.
Substitute y = 40 into the first equation (0.3x + 0.2y = 5):
0.3x + 0.2(40) = 5
0.3x + 8 = 5
0.3x = -3
Divide both sides by 0.3 to solve for x:
x = -3 / 0.3
x = -10
The solution to the system of equations is x = -10 and y = 40.