Question

Use the system of equations to answer the questions. 2x + 3y = 3 y = 8 – 3x The value of y from the second equation is substituted back into the first equation. What is the resulting equation? What is the value of x? What is the value of y?

Answer 1

1. 2x + 3 (8-3x) = 3

2. 3

3. -1

Answer 2

Answer:

Given the system of equation:

2x+3y=3                    ......[1]

y=8-3x                       ......[2]

as per the given condition;

Substitute the value of y from the equation [2] into the [1] equation;

$2x+3(8-3x) =3$

Using distributive property on LHS, (i.e, $a\cdot(b+c) = a\cdot b+ a\cdot c$ )

$2x+3\cdot 8+ 3 \cdot (-3x) =3$ or

2x+24-9x =3

Combine like terms;

$-7x+24 =3$

Subtract 24 from both the sides,

$-7x+24-24=3-24$

Simplify:

-7x =-21

Divide by -7 to both sides of an equation;

$\frac{-7x}{-7} = \frac{-21}{-7}$

Simplify:

x =3

Substitute the value of x =3 in equation [2] to solve for y;

$y=8-3(3) =8 -9 =-1$

Hence, the answer for this question is:

The resulting equation is: $2x+3(8-3x) =3$

And the value of x =3 and that of y = -1