Solving equations using subsitution practic
1. Solve the following equation by substitution method:
3x + 2y = 8
2x - y = 1
Step 1: Solve the second equation for y:
2x - y = 1
y = 2x - 1
Step 2: Substitute the value of y from the second equation into the first equation:
3x + 2(2x - 1) = 8
3x + 4x - 2 = 8
7x - 2 = 8
7x = 10
x = 10/7
Step 3: Substitute the value of x back into the second equation to solve for y:
2(10/7) - y = 1
20/7 - y = 1
-y = 1 - 20/7
-y = 7/7 - 20/7
-y = -13/7
y = 13/7
Therefore, the solution to the system of equations is x = 10/7 and y = 13/7.
2. Solve the following equation by substitution method:
2x + 3y = 11
x - 2y = -3
Step 1: Solve the second equation for x:
x = 2y - 3
Step 2: Substitute the value of x from the second equation into the first equation:
2(2y - 3) + 3y = 11
4y - 6 + 3y = 11
7y - 6 = 11
7y = 17
y = 17/7
Step 3: Substitute the value of y back into the second equation to solve for x:
x - 2(17/7) = -3
x - 34/7 = -3
x = -3 + 34/7
x = -21/7 + 34/7
x = 13/7
Therefore, the solution to the system of equations is x = 13/7 and y = 17/7.