Solve the following systems of equations. If the system cannot be solved ,state that it cannot be solved and explain why.

Question

Solve the following systems of equations. If the system cannot be solved ,state that it cannot be solved and explain why.

1.3x+y=7
3x+y=10

2. 5x-2y=-24
-4y=-48-10x

Answer 1

I found out that question 2 is the same equation so it can't be solved but I still need help with question 1.

Answer 2

To solve the first system of equations:

1.3x + y = 7
3x + y = 10

We can use the method of elimination to solve this system. The goal is to eliminate one variable by adding or subtracting the two equations.

Step 1: To eliminate y, let's subtract the first equation from the second equation.
(3x + y) - (1.3x + y) = 10 - 7
2x = 3

Step 2: Divide both sides of the equation by 2 to isolate x.
x = 3/2 or 1.5

Step 3: Now that we have the value of x, we can substitute it into any of the two original equations to find the value of y. Let's use the first equation.
3(1.5) + y = 10
4.5 + y = 10
y = 10 - 4.5
y = 5.5

Therefore, the solution to the first system of equations is x = 1.5 and y = 5.5.

To solve the second system of equations:
5x - 2y = -24
-4y = -48 - 10x

We have two equations, but they are not in standard form (Ax + By = C), so we need to rearrange them first.

First Equation:
5x - 2y = -24
We can leave it as it is.

Second Equation:
-4y = -48 - 10x
Let's multiply every term by -1 and flip the direction of the inequality sign.
4y = 48 + 10x

Step 1: Now we can apply the method of substitution. Solve either equation for one variable and substitute that expression into the other equation.

From the first equation:
5x - 2y = -24
-2y = -5x - 24
y = (5/2)x + 12

Step 2: Substitute this expression for y in the second equation:
4y = 48 + 10x
4((5/2)x + 12) = 48 + 10x
10x + 48 = 48 + 10x

Step 3: Simplify the equation.
10x cancels out on both sides.
48 = 48

The equation simplifies to 48 = 48, which is always true. This means that the variables cancel out, and we are left with an identity.

Conclusion:
The second system of equations doesn't have a unique solution. It is considered an inconsistent system because the equations represent parallel lines that do not intersect.