Question

question
solve the system of equations using elimination: $4x + 3y = -5$ and $-5x - 9y = 22$.

Explanation:

Step1: Multiply first equation to eliminate y

To eliminate \( y \), we can multiply the first equation \( 4x + 3y = -5 \) by 3. This gives:
\( 3\times(4x + 3y) = 3\times(-5) \)
\( 12x + 9y = -15 \)

Step2: Add the two equations

Now we have the two equations:
\( 12x + 9y = -15 \) (from Step 1)
\( -5x - 9y = 22 \) (original second equation)

Add them together:
\( (12x + 9y) + (-5x - 9y) = -15 + 22 \)
Simplify: \( 12x - 5x + 9y - 9y = 7 \)
\( 7x = 7 \)

Step3: Solve for x

Divide both sides by 7:
\( x = \frac{7}{7} = 1 \)

Step4: Substitute x back to find y

Substitute \( x = 1 \) into the first original equation \( 4x + 3y = -5 \):
\( 4(1) + 3y = -5 \)
\( 4 + 3y = -5 \)

Subtract 4 from both sides:
\( 3y = -5 - 4 \)
\( 3y = -9 \)

Divide by 3:
\( y = \frac{-9}{3} = -3 \)

Answer:

The solution to the system is \( x = 1 \) and \( y = -3 \), or the ordered pair \( (1, -3) \).