Solve by the substitution method:
solve what?
To solve a 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.
Step 2: Substitute the expression found in Step 1 into the other equation.
Step 3: Solve the resulting equation from Step 2 for the remaining variable.
Step 4: Substitute the value found in Step 3 back into either of the original equations to find the value of the other variable.
Step 5: Check the solution by substituting the found values of the variables into both original equations.
Without the specific equations provided, I cannot solve by substitution, but I can guide you through an example. Let's say we have the following equations:
Equation 1: 2x + y = 5
Equation 2: 3x - 2y = -8
Step 1: Solve Equation 1 for x:
2x = 5 - y
x = (5 - y) / 2
Step 2: Substitute the expression x = (5 - y) / 2 into Equation 2:
3((5 - y) / 2) - 2y = -8
Step 3: Solve the resulting equation from Step 2 for y:
(15 - 3y) / 2 - 2y = -8
Multiply both sides by 2 to eliminate the fraction:
15 - 3y - 4y = -16
Combine like terms:
-7y = -16 - 15
-7y = -31
Divide both sides by -7:
y = 31 / 7
y = 4.43 (rounded to two decimal places)
Step 4: Substitute the value of y back into Equation 1:
2x + 4.43 = 5
2x = 5 - 4.43
2x = 0.57
x = 0.57 / 2
x = 0.285 (rounded to three decimal places)
Step 5: Check the solution by substituting the values of x and y into both original equations:
Equation 1: 2(0.285) + 4.43 ≈ 5 (approximately)
Equation 2: 3(0.285) - 2(4.43) ≈ -8 (approximately)
Thus, the solution to the system of equations is x ≈ 0.285 and y ≈ 4.43.