please solve by method of substitution
0.3x-0.4y-0.33=0
0.1x + 0.2y -.21=0
please give all steps to solve.I think I understand the basic concept but this is little more complicated for me. Thanks in advance
Things look a lot easier if you multiply each equation by 100 and simplify, and transpose the constants to the right hand side.
30x - 40y = 33 .....(1)
10x + 20y = 21 .....(2)
From equation (2), transpose 20y to the right and divide equation by 10 to get
10x = 21 - 20y
x = 2.1 -2y .... (3)
Substitute x into equation (1) to get
30(2.1-2y) - 40y = 33
63 - 60y -40y = 33
-100y = 33-63
-100y = -30
y=(-30)/(-100)
=0.3
Substitute y=0.3 into (3) to get
x=2.1-2(0.3)
=1.5
Now, substitute these values of x=1.5 and y=0.3 into the original equations to make sure the solution is correct.
To solve the system of equations using the method of substitution, follow these steps:
Step 1: Solve one equation for one variable
Pick one of the equations and solve it for one variable in terms of the other variable. Let's choose the first equation to solve for x:
0.3x - 0.4y - 0.33 = 0
Rearrange the equation:
0.3x = 0.4y + 0.33
Divide every term by 0.3 to isolate x:
x = (0.4y + 0.33) / 0.3
Step 2: Substitute the expression from step 1 into the second equation
Now substitute the expression for x, which we found in step 1, into the second equation:
0.1x + 0.2y - 0.21 = 0
Replace x with (0.4y + 0.33) / 0.3 in the equation:
0.1 * ((0.4y + 0.33) / 0.3) + 0.2y - 0.21 = 0
Step 3: Simplify and solve for y
Simplify the equation by multiplying through by 0.3 to eliminate the fraction:
0.1 * (0.4y + 0.33) + 0.6y - 0.63 = 0
Distribute the 0.1:
0.04y + 0.033 + 0.6y - 0.63 = 0
Combine like terms:
0.64y - 0.597 = 0
Add 0.597 to both sides:
0.64y = 0.597
Divide both sides by 0.64:
y = 0.597 / 0.64
Simplify:
y ≈ 0.933
Step 4: Substitute y value back into the expression for x
Finally, substitute the value of y back into the expression we found for x in step 1:
x = (0.4y + 0.33) / 0.3
x = (0.4 * 0.933 + 0.33) / 0.3
Simplify:
x ≈ 1.133
Therefore, the solution to the system of equations is approximately x ≈ 1.133, y ≈ 0.933.