Question

Part 1: Explain, in complete sentences, how you would use the substitution method to solve the following system of equations. (3 points)

Part 2: Provide the solution to the system. (1 point)

5x – y = –2
10x – 3y = –7

Answer 1

From Eq 1 y=5x+2
Put it in Eq 2
10x-15x-6=-7
x=1/5

Answer 2

5x – y = –2
10x – 3y = –7

1. Write the first equation in the following form:
5x + 2 = y

2. Substitute the expression 5x+2 in place of y in the second equation:
10x - 3(5x+2) = -7

3. Simplify the left side of that equation:

10x - 15x -6 = -7
-5x - 6 = -7

4. Continue Solving for x:

-5x = -7+6
-5x = -1
x = 1/5

5. Substitute the value for x back into the first equation:
5(1/5) - y = -2
1 - y = -2
1 + 2 = y
3 = y

6. Check using the second equation:

10(1/5) - 3(3) = -7
2 -9 = -7
-7 = -7