System of Equations|Please help!

Question

3x + 4y = -23

2y - x = -19

What is the solution (x, y) to the system of equations above?

Answer 1

An alternative, potentially more efficient way via elimination

3x+4y=−23 (1)

2y−x=−19 (2)

Multiple equation (2) by 2. Then SUBTRACT the two equations: (1)-(2). The y terms should cancel out.

OR

Multiple equation (2) by 3. Then ADD the two equations: (1)+(2). The x terms should cancel out.

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Answer 2

Here is how I would solve the system. Since it is easy to isolate the variable x in the 2nd equation, I would solve that equation for x in terms of y, and then substitute for x in the 1st equation.

2 y - x = -19

2y + 19 = x

x = 2y + 19

Here is the first equation:

3x + 4y = -23

3(2y + 19) + 4y = -23 (substitution for equality--replace x with its equivalent expression from 2nd equation)

6y + 57 + 4y = -23

10y + 57 = -23

10y = -23 - 57

10y = -80

y = -8

Now that we know the value for y that makes both equations true, substitute that value for y in one of the above equations and solve for x. Since we have x = 2y + 19:

x = 2(-8) + 19

x = -16 + 19

x = 3

So the ordered pair (x, y) that makes both equations true is: (3, -8). If you graph both lines on the same coordinate system, that point is where the lines intersect.

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Answer 3

To solve this system of equations:

1. Given equations:
2. 3x + 4y = -23
3. 2y - x = -19
4. Solve for x in the second equation:
5. 2y - x = -19
6. Add x to both sides: 2y = x - 19
7. Rearrange: x = 2y + 19
8. Substitute x into the first equation:
9. 3(2y + 19) + 4y = -23
10. Expand: 6y + 57 + 4y = -23
11. Combine like terms: 10y + 57 = -23
12. Subtract 57 from both sides: 10y = -80
13. Divide by 10: y = -8
14. Find x using x = 2y + 19:
15. x = 2(-8) + 19
16. x = -16 + 19
17. x = 3
18. Final Answer: (x, y) = (3, -8) ✅

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Answer 4

1. 3x+4y=−23
2. 2y−x=−19

First, solve the second equation

2y −x = −19 ⇒ x = 2y + 19

Now, substitute this expression into the first (1) equation:

3(2y+19)+4y=−23

Expand the equation:

6y+57+4y=−23

Combine like terms:

10y+57=−23

Subtract 57 from both sides:

10y=−80

Divide by 10:

y=−8

Now substitute y=−8 into the expression x=2y+19

x=2(−8)+19

x= −16+19

x=3

So, the solution is x=3 and y=−8.

The solution is (x,y)=(3,−8)