Problem 1 :
Solve the following system of equations by substitution method.
2x - 3y = -1 and y = x - 1
Solution :
2x - 3y = -1 -----(1)
y = x - 1 -----(2)
Step 1 :
From (2), substitute (x - 1) for y into (1).
(1)-----> 2x - 3(x - 1) = -1
Simplify.
2x - 3x + 3 = -1
-x - 3 = -1
Add 3 to each side.
-x = 2
Multiply each side (-1).
x = -2
Step 2 :
Substitute -2 for x into (2).
(2)-----> y = 2 - 1
y = 1
Therefore, the solution is
(x, y) = (-2, 1)
Problem 2 :
Solve the following system of equations by substitution method.
y = -3x + 5 and 5x - 4y = -3
Solution :
y = -3x + 5 -----(1)
5x - 4y = -3 -----(2)
Step 1 :
From (1), substitute (-3x + 5) for y into (2).
(2)-----> 5x - 4(-3x + 5) = -3
Simplify.
5x + 12x - 20 = -3
17x - 20 = -3
Add 20 to each side.
17x = 17
Divide each side by 17.
x = 1
Step 2 :
Substitute 1 for x into (1).
(1)-----> y = -3(1) + 5
y = -3 + 5
y = 2
Therefore, the solution is
(x, y) = (1, 2)
Problem 3 :
Solve the following system of equations by substitution method.
y = 5x - 7 and -3x - 2y = -12
Solution :
y = 5x - 7 -----(1)
-3x - 2y = -12 -----(2)
Step 1 :
From (1), substitute (5x - 7) for y into (2).
(2)-----> -3x - 2(5x - 7) = -12
Simplify.
-3x - 10x + 14 = -12
-13x + 14 = -12
Subtract 14 from each side.
-13x = -26
Divide each side by -13.
x = 2
Step 2 :
Substitute 2 for x into (1).
(1)-----> y = 5(2) - 7
y = 10 - 7
y = 3
Therefore, the solution is
(x, y) = (2, 3)
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