Solve using the substitution method.
0.3x+0.2y=5,0.5x+0.4y=11
I would multiply each equation by 10 to get rid of those decimals
3x + 2y = 50 ---> 2y = 50-3x
5x + 4y = 110
sub 2y= 50-3x into the 2nd
5x + 2(50-3x) = 110
5x + 100 - 6x = 110
-x = 10
x = -10
into 2y = 50-3x = 50-3(-10)
2y = 80
y = 40
x = -10, y = 40
To solve this system of equations using the substitution method, we can solve one equation for one variable and then substitute that expression into the other equation.
Let's start with the first equation: 0.3x + 0.2y = 5.
Step 1: Solve for x in terms of y:
0.3x = 5 - 0.2y
x = (5 - 0.2y) / 0.3
Now we can substitute this expression for x into the second equation: 0.5x + 0.4y = 11.
Step 2: Substitute x in terms of y into the second equation:
0.5((5 - 0.2y) / 0.3) + 0.4y = 11
Now we have an equation with only one variable, y. Let's simplify and solve for y.
Step 3: Simplify the equation:
(0.5(5 - 0.2y) / 0.3) + 0.4y = 11
(2.5 - 0.1y) / 0.3 + 0.4y = 11
(2.5 - 0.1y) + 0.4y * 0.3 = 11
Step 4: Continue simplifying the equation:
2.5 - 0.1y + 0.12y = 11
2.5 + 0.02y = 11
Step 5: Isolate the y term:
0.02y = 11 - 2.5
0.02y = 8.5
Step 6: Solve for y by dividing both sides by 0.02:
y = 8.5 / 0.02
Now that we have found 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: 0.3x + 0.2y = 5.
Step 7: Substitute the value of y into the equation:
0.3x + 0.2(8.5 / 0.02) = 5
Step 8: Simplify and solve for x:
0.3x + 17 = 5
0.3x = 5 - 17
0.3x = -12
x = -12 / 0.3
x = -40
Therefore, the solution to the system of equations is x = -40 and y = 425/2.