Question

8x + 4y= 12
2x + y= 3

Answer 1

`\tt Step-by-step~explanation:`

In order to solve for both x and y, we need to use the substitution property, where we replace a variable with what we solved for.

`\tt Step~1:`

Let's solve for y first. Equation (1st one): 8x + 4y = 12. To isolate y, we can first subtract 8x from both sides, and then divide all terms by 4.

`\tt 8x- (8x)+4y=12-(8x)\\4y=12-8x\\4y/4=y\\12/4=3\\-8x/4=-2x\\y=3-2x`

`\tt Step~2:`

Then, we can solve for x. Let's take the second equation: 3x + y = 3. We take what we solved for in the previous step and plug it into this equation.

`\tt 2x+(3-2x)=3\\2x+3-2x=3\\2x-2x=0\\3-3=0\\0=0\\x=x`

`\large\boxed{\tt Our ~final~answer:(x,3-2x)}`

Both equations are also the same, so the solution = all real numbers for x.

`\tt y=3-2x\\3-2x=3-2x`

Answer 2

The system is dependent, and the solution is an infinite set of points that lie on the line 2x + y = 3.

To determine the value of x and y using simultaneous equation

8x + 4y = 12 ---(1)

2x + y = 3 ---(2)

Using the substitution method of simultaneous equation,

From equation (2), solve for y = 3 - 2x

Substitute the expression for y into equation (1):

8x + 4(3 - 2x) = 12

8x + 12 - 8x = 12

8x - 8x = 12 - 12

The equation simplifies to a true statement, which means the system is dependent. The solution is an infinite set of points that lie on the line 2x + y = 3. The system does not have a unique solution