Question

Given a system of linear equations, solve using substitution y-4=2(x 3) -4x 6y=12

Answer 1

To solve the system of linear equations using substitution method, solve one equation for one variable and substitute that expression into the other equation. The solution is x = 2 and y = 2.

Step-by-step explanation:

To solve the system of linear equations using substitution method, we will solve one equation for one variable and substitute that expression into the other equation.

Given equations:

y - 4 = 2x - 6 ---------------(1)

6y = 12 ---------------(2)

From equation (2), we can find the value of y:

6y = 12

y = 12/6

y = 2

Now, substitute the value of y into equation (1):

y - 4 = 2x - 6

2 - 4 = 2x - 6

-2 = 2x - 6

2x = -2 + 6

2x = 4

x = 4/2

x = 2

So, the solution to the system of equations is x = 2 and y = 2.

Answer 2

The solution to the system of linear equations is x = 4 and y = 2. ​

How to solve linear equations?

To solve the given system of linear equations using substitution, rewrite the equations in a clear format. The equations seem to be:

1. y - 4 = 2(x + 3) - 4x

2. 6y = 12

Start by simplifying each equation and then use substitution to find the values of x and y.

First, simplify Equation 1:

y - 4 = 2x + 6 - 4x

Now, simplify Equation 2:

6y = 12

`\[ y = (12)/(6) = 2 \]`

Substitute y = 2 into y = -2x + 10:

`\[ 2 = -2x + 10 \]`

Solve for x:

`\[ -2x = 2 - 10 \]`

`\[ -2x = -8 \]`

`\[ x = (-8)/(-2) \]`

x = 4

Therefore, the solution to the system of equations is x = 4 and y = 2.