3x + 4y = -2

2y – x = -19

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

Select one:

a.  (9,-6)

b. (2,-4)

c. (4,-6)

d.  (3,-8)

e. (-5,-2)

We have the system of equations:

1. \( 3x + 4y = -2 \)
2. \( 2y - x = -19 \)

Let's solve this system step-by-step.

### Step 1: Rearrange the second equation
From the second equation, \( 2y - x = -19 \), solve for \( x \):

\[
x = 2y + 19
\]

### Step 2: Substitute this into the first equation
Substitute \( x = 2y + 19 \) into the first equation:

\[
3(2y + 19) + 4y = -2
\]

### Step 3: Simplify and solve for \( y \)
Expand the equation:

\[
6y + 57 + 4y = -2
\]

Combine like terms:

\[
10y + 57 = -2
\]

Subtract 57 from both sides:

\[
10y = -2 - 57
\]
\[
10y = -59
\]

Divide by 10:

\[
y = -\frac{59}{10}
\]

### Step 4: Find \( x \)
Now, substitute \( y = -\frac{59}{10} \) back into \( x = 2y + 19 \) to find \( x \):

\[
x = 2\left(-\frac{59}{10}\right) + 19 = -\frac{118}{10} + 19 = -11.8 + 19 = 7.2
\]

Therefore, the solution is \( x = 7.2 \), \( y = -5.9 \).



3x + 4y = -2

2y – x = -19

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

This page explains how to solve the system of equations 3x + 4y = -2 and 2y - x = -19 using the substitution method. A step-by-step approach demonstrates the key algebraic concepts and theorems involved, making it suitable for students in Grades 8-10.

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