Question

A pair of equations is shown below:

y=7x-5
y=3x+3
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (7 points)
Part B: Check your work. Verify your solution and show your work. (2 points)
Part C: If the two equations are graphed, what does your solution mean?

Answer 1

Part A: y = 9; x = 2

Part B: Our solutions are correct.

Part C: Our solution represents the coordinates of the intersection of the two equations in the system of equations

Explanation:

Part A:

Method to solve: We can solve the system of equations using elimination.

Step 1: Multiply the first equation by -3 and the second equation by 7:

-3(y = 7x - 5)

-3y = -21x + 15

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7(y = 3x + 3)

7y = 21x + 21

Step 2: Add the two equations made when multiplying the first by -3 and the second and 7 to cancel out the x:

-3y = -21x + 15

+ 7y = 21x + 21

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4y = 36

Step 3: Divide both sides by 4 to find y:

(4y = 36) / 4

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y = 9

Step 4: Plugi in 4 for y in y = 7x -5 to find x:

9 = 7x - 5

Step 5: Add 5 to both sides:

(9 = 7x - 5) + 5

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14 = 7x

Step 6: Divide both sides by 7 to find x:

(14 = 7x) / 7

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2 = x

Thus, y = 9 and x = 2.

Part B:

Step 1: Plug in 9 for y and 2 for x in y = 7x - 5 and simplify:

When we plug in 9 for y and 2 for x, we must get 9 on both sides of the equation in order for our answer to be correct:

9 = 7(2) - 5

9 = 14 - 5

9 = 9

Step 2: Plug in 9 for y and 2 for x in y = 3x +3 and simplify:

9 = 3(2) + 3

9 = 6 + 3

9 = 9

Thus, our answers are correct and we've found the correct solution to the system of equations.

Part C:

When a system of equations is graphed, the solution to the system is always the coordinates of the intersection of the two equations in the system. Thus, our solution represents the coordinates of the intersection of the two equations in the system of equations.