Question

elimination with multiplication
question 8 of 10 (1 point) | question attempt: 1 of
solve the following system of equations.
5x + 3y = 9
-7x - 9y = 21
x =
y =

Explanation:

Step1: Multiply first equation

To eliminate \( y \), multiply the first equation \( 5x + 3y = 9 \) by \( 3 \). We get \( 3(5x + 3y)=3\times9 \), which simplifies to \( 15x + 9y = 27 \).

Step2: Add to second equation

Now add this new equation to the second equation \( -7x - 9y = 21 \). So, \( (15x + 9y)+(-7x - 9y)=27 + 21 \). The \( y \)-terms cancel out: \( 15x-7x+9y - 9y=48 \), which simplifies to \( 8x = 48 \).

Step3: Solve for \( x \)

Divide both sides of \( 8x = 48 \) by \( 8 \): \( x=\frac{48}{8}=6 \).

Step4: Substitute \( x \) to find \( y \)

Substitute \( x = 6 \) into the first original equation \( 5x + 3y = 9 \). We have \( 5\times6+3y = 9 \), which is \( 30 + 3y = 9 \). Subtract \( 30 \) from both sides: \( 3y=9 - 30=-21 \). Then divide by \( 3 \): \( y=\frac{-21}{3}=-7 \).

Answer:

\( x = 6 \), \( y = -7 \)