Question

Complete the statements about the system of linear equations represented by the tables. The equation representing the left table is y = 1.5x - Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 1. Isolate x in the first equation: 2. Substitute the value for x into the second equation: 3. Solve for y: 4. Substitute y into either original equation: 5. Write the solution as an ordered pair: x = 7 – 3y 2(7 – 3y) + 4y = 8 14 – 6y + 4y = 8 14 – 2y = 8 –2y = –6 y = 3 x + 3(3) = 7 ( , )

Answer 1

1. To isolate x in the first equation, x + 3y = 7, we can subtract 3y from both sides:
x = 7 - 3y

2. Now, let's substitute the value for x into the second equation, 2x + 4y = 8:
2(7 - 3y) + 4y = 8

3. Simplifying the equation:
14 - 6y + 4y = 8
14 - 2y = 8

4. To solve for y, we can subtract 14 from both sides:
-2y = -6

5. Dividing both sides by -2, we find:
y = 3

6. Now, let's substitute the value of y into either of the original equations. Let's use x + 3y = 7:
x + 3(3) = 7
x + 9 = 7
x = -2

7. The solution to the system of equations is the ordered pair (x, y), which in this case is (-2, 3).

Hope that helps!