Question

Which value of x satisfies both -9x+4y=8 and -3x-y=4 given the same value of y?

Answer 1

The value of x satisfies both -9x + 4y = 8 and -3x - y = 4 given the same value of y is  $-\frac{8}{7}$

Step-by-step explanation:

The system of equations has two equations:

• -9x + 4y = 8
• -3x - y = 4

Let us solve the system of equations to find the value of x and substitute it in the two equations to check if it gives the same value of y in the two equations

∵ -9x + 4y = 8 ⇒ (1)

∵ -3x - y = 4 ⇒ (2)

- Multiply equation (2) by 4 to make the coefficients of y in the

  two equations have same value and different signs

∴ -12x - 4y = 16 ⇒ (3)

- Add equations (1) and (3) to eliminate y

∴ -21x = 24

- Divide both sides by -21

∴ x = $-\frac{8}{7}$

Let us substitute this value of x in equations (1) and (2) to find y

∵ -9( $-\frac{8}{7}$ ) + 4y = 8

∴ $\frac{72}{7}$ + 4y = 8

- Subtract  $\frac{72}{7}$  from both sides

∴ 4y = $-\frac{16}{7}$

- Divide both sides by 4

∴ y = $-\frac{4}{7}$

∵ -3( $-\frac{8}{7}$ ) - y = 4

∴ $\frac{24}{7}$ - y = 4

- Subtract   $\frac{24}{7}$  from both sides

∴ - y = $\frac{4}{7}$

- Divide both sides by -1

∴ y = $-\frac{4}{7}$

The value of x satisfies both -9x + 4y = 8 and -3x - y = 4 given the same value of y is  $-\frac{8}{7}$

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

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