y=4x-1
y=2x-5
Use substitution to solve each system of equations
You know y=4x-1. Put that in for y in the second equation.
4x-1=2x-5
solve for x
Unit 4: Solving System of Equations with Substitution
To solve the given system of equations using the method of substitution, we will substitute one equation into the other and solve for the variable.
Step 1: We have the two equations:
y = 4x - 1 ...(Equation 1)
y = 2x - 5 ...(Equation 2)
Step 2: We can express Equation 1 in terms of y, and then substitute it into Equation 2.
From Equation 1, rearrange to solve for x:
4x = y + 1
x = (y + 1)/4
Step 3: Substitute the value of x from Equation 1 into Equation 2.
In Equation 2, replace x with (y + 1)/4:
y = 2((y + 1)/4) - 5
Simplify:
y = (y + 1)/2 - 5
Step 4: Solve the equation obtained in Step 3 for y.
Multiply everything by 2 to eliminate the fraction:
2y = y + 1 - 10
2y - y = -9
y = -9
Step 5: Find the value of x using the value of y found in Step 4.
Using Equation 1, substitute y = -9:
x = (y + 1)/4
x = (-9 + 1)/4
x = -2
Step 6: Verify the solution by substituting the values of x and y into both equations.
Using Equation 1: -9 = 4(-2) - 1
-9 = -8 - 1
-9 = -9 (true)
Using Equation 2: -9 = 2(-2) - 5
-9 = -4 - 5
-9 = -9 (true)
Therefore, the solution to the given system of equations is x = -2 and y = -9.