Question

What is the best first step for solving the given system using substitution while avoiding fractions? =9x+4x=10 -9x+3y=3

Solve for x in the first equation.
Solve for y in the first equation.
Solve for x in the second equation.
Solve for y in the second equation.

Answer 1

Solve for y in the second equation

D is correct

Explanation:

Given: 9x+4y=10 and -9x+3y=3 system of equation.

We are given system of equation in x and y form of straight line.

We need to solve for x and y without using fraction.

We will choose those equation has common factor.

If we pick first equation coefficients are 9,4 and 10.

Here, no any common factor.

Now we pick second equation.

-9x+3y=3

Common factors of coefficients are 3

If we divide each term by 3 we will get coefficient of y be 1 and rest are not in fraction.

So, we will pick second equation and solve for y.

-9x + 3y = 3

Divide by 3 both sides to each term

-3x + y = 1

Add 3x both sides

y = 3x + 1

So, we get y = 3x + 1 . In this equation none is fraction term.

Answer 2

Solve for y in the second equation

Explanation:

We assume your system is ...

• -9x +4y = 10
• -9x +3y = 3

Dividing the second equation by 3 gives ...

-3x +y = 1

so an expression for y without fractions can be found by solving for y, that is, by adding 3x:

y = 3x +1

_____

Comment on alternate solution

We'd be tempted to solve the first equation for -9x and substitute for that.

-9x = 10 -4y

(10 -4y) +3y = 3 . . . . . substitute for -9x

-y = -7 . . . . . . . . . . . . . simplify, subtract 10

y = 7 . . . . . . . . . . . . . . multiply by -1