Question

Which first step for solving the given system using substitution results in an equation without fractions?

Answer 1

Answer:

The step to take to avoid fraction is to solve for y in equation 2

Step-by-step explanation:

Given

-9x+ 4y =- 10

-9x+ 3y = 3

Required:

Step for solving using substitution (avoiding fraction)

Let -9x+ 4y =- 10  represent equation 1

and -9x+ 3y = 3 represent equation 2

The following points are to be noted

• Solving for x or y in equation 1 will definitely lead to having fractions

• Solving for x in equation 2 will also lead to having fractions

Having said that, the step to take to avoid fraction is to solve for y in equation 2

Check

$-9x+ 3y = 3$

Add 9x to both sides

$9x-9x+ 3y = 3 + 9x$

$3y = 3 + 9x$

Divide through by 3

$\frac{3y}{3} = \frac{3 + 9x}{3}$

$y = \frac{3 + 9x}{3}$

Split fraction

$y = \frac{3}{3} + \frac{9x}{3}$

$y = 1 + 3x$

At the point, the expression of y can then be substituted in equation 1