4x - y = 2, 9x - 2y = 8 find solution
by substitution method
i need help want math
To solve the given 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.
Let's solve the first equation for x:
4x - y = 2
First, isolate x by moving -y to the right side:
4x = y + 2
Now divide by 4:
x = (y + 2)/4
Step 2: Substitute the expression obtained in step 1 into the other equation.
Replace x in the second equation with (y + 2)/4:
9((y + 2)/4) - 2y = 8
Step 3: Simplify and solve for y.
Multiply both sides by 4 to eliminate the fraction:
9(y + 2) - 8y = 32
9y + 18 - 8y = 32
y + 18 = 32
y = 32 - 18
y = 14
Step 4: Substitute the value of y back into one of the original equations to find x.
Use the first equation:
4x - y = 2
Substitute y = 14:
4x - 14 = 2
4x = 16
x = 16/4
x = 4
Step 5: Verify the solution by substituting the values of x and y back into both original equations.
For the first equation: 4x - y = 2
4(4) - 14 = 2
16 - 14 = 2
2 = 2 (True)
For the second equation: 9x - 2y = 8
9(4) - 2(14) = 8
36 - 28 = 8
8 = 8 (True)
Hence, the solution to the system of equations is x = 4 and y = 14.