Question

elimination with multiplication
question 9 of 10 (1 point) | question attempt: 1 of 3

solve the following system of equations.
-8x - 9y = 17
-3x - 4y = 7

x =

y =

Explanation:

Step1: Multiply equations to eliminate a variable

We have the system:

$$\begin{cases} -8x - 9y = 17 \quad (1) \\ -3x - 4y = 7 \quad (2) \end{cases}$$

Multiply equation (1) by 3 and equation (2) by 8 to make the coefficients of \(x\) equal (in absolute value):
Equation (1) becomes: \(3\times(-8x - 9y)=3\times17\) → \(-24x - 27y = 51\) \((1a)\)
Equation (2) becomes: \(8\times(-3x - 4y)=8\times7\) → \(-24x - 32y = 56\) \((2a)\)

Step2: Subtract equations to eliminate \(x\)

Subtract \((1a)\) from \((2a)\):
\((-24x - 32y)-(-24x - 27y)=56 - 51\)
Simplify: \(-24x - 32y + 24x + 27y = 5\) → \(-5y = 5\)

Step3: Solve for \(y\)

Divide both sides by \(-5\): \(y=\frac{5}{-5}=-1\)

Step4: Substitute \(y\) into an equation to find \(x\)

Substitute \(y = -1\) into equation (2): \(-3x - 4\times(-1)=7\)
Simplify: \(-3x + 4 = 7\)
Subtract 4 from both sides: \(-3x = 7 - 4 = 3\)
Divide by \(-3\): \(x=\frac{3}{-3}=-1\)

Answer:

\(x = -1\), \(y = -1\)