Final answer:
To solve the system of linear equations with decimal coefficients, we can use the elimination method. Multiply the equations by multiples to make the coefficients of x or y in one equation equal to the coefficients in the other equation, then subtract or add the equations to eliminate one variable. Finally, solve for the remaining variable and substitute it back into one of the original equations to find the value of the other variable.
Step-by-step explanation:
To solve the system of equations with decimal coefficients, we can use the method of substitution or elimination. Let's use the elimination method to solve this system. We'll multiply both equations by multiples and make the coefficients of x or y in one equation equal to the coefficients in the other equation. After that, we'll subtract or add the two equations to eliminate one variable. Finally, we'll solve for the remaining variable and substitute it back into one of the original equations to find the value of the other variable.
First, let's multiply the first equation by 100 to eliminate the decimals:
6x + 32y = 28
Now, let's multiply the second equation by 1000 to eliminate the decimals:
70x + 80y = 580
Now we have two equations:
6x + 32y = 28
70x + 80y = 580
We can multiply the first equation by 10 and the second equation by 3 to make the coefficients of y equal:
60x + 320y = 280
210x + 240y = 1740
Now we can subtract the two equations:
(210x + 240y) - (60x + 320y) = 1740 - 280
150x - 80y = 1460
Simplifying this equation, we get:
150x - 80y = 1460
Now we can solve for y:
-80y = 1460 - 150x
y = (1460 - 150x) / -80
Now we substitute this value of y into one of the original equations to find x. Let's use the first equation:
0.06x + 0.32((1460 - 150x) / -80) = 0.28
Now we solve for x by multiplying through by -80 to eliminate the fraction:
-4.8x - 37.6 + 0.32(1460 - 150x) = 0.28(-80)
-4.8x - 37.6 + 467.2 - 48x = -22.4
Combine like terms:
-52.8x + 429.6 = -22.4
-52.8x = -22.4 - 429.6
-52.8x = -452
Simplifying this equation, we get:
x = -452 / -52.8
x = 8.54
Now substitute this value of x back into one of the original equations to find y. Let's use the first equation:
0.06(8.54) + 0.32y = 0.28
0.5124 + 0.32y = 0.28
0.32y = 0.28 - 0.5124
0.32y = -0.2324
Simplifying this equation, we get:
y = -0.2324 / 0.32
y = -0.72625
Therefore, the solution to the system of equations is x = 8.54 and y = -0.72625.
Learn more about Solving systems of linear equations with decimal coefficients