Question

explain how to solve a system of equations using the substitution method. Use y=3-3x and 3x+4y=6

Answer 1

$y = 3 - 3x \: \: \: \: (1)\\ \\ 3x + 4y = 6 \: \: \: \: (2)$

Put value of y into 2 equation

$3x + 4(3 - 3x) = 6 \\ \\ 3x + 12 - 12x = 6 \\ \\ 9x = 6 \\ \\ x = \frac{</strong><strong>2</strong><strong>}{</strong><strong>3</strong><strong>}$

Now put value of x in any equation to find y

$y = 3 - 3x \\ \\ y = 3 - 3 \times \frac{</strong><strong>2</strong><strong>}{</strong><strong>3</strong><strong>} \\ \\ y = 1$

Answer 2

Given equations,

3x + 4y = 6 _____________________1

y = 3 - 3x

y- 3 = -3x

3 - y = 3x

Now, substitute the value of 3x in equation (1)

We get, (3-y) + 4y = 6

3 - y + 4y = 6

3 + 3y = 6

3y = 6 - 3

3y = 3

y = 1

Put value of y in any of the equation and we will get value of x.

3 - y = 3x

3 - 1 = 3x

2 = 3x

2/3 = x

Hence, y = 1 and x = 2/3

Hope it helps