Question

Solve the system by substitution
-4.5x-2y=-12.5
3.25x-y=-0.75

Answer 1

To solve the system of equations by substitution, choose one equation to solve for one variable in terms of the other, substitute this expression into the other equation, solve for the remaining variable, and substitute the value back into any of the original equations to find the value of the other variable. The solution to the given system of equations is (1, 3.5).

Step-by-step explanation:

To solve the system of equations by substitution, follow these steps:

1. Choose one equation to solve for one variable in terms of the other.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute this value back into any of the original equations to find the value of the other variable.
5. Write the solution as an ordered pair (x, y).

For the given system:

-4.5x-2y=-12.5

3.25x-y=-0.75

First, let's solve the second equation for y:

y = 3.25x + 0.75

Next, substitute this expression for y in the first equation:

-4.5x - 2(3.25x + 0.75) = -12.5

Simplify and solve for x:

-4.5x - 6.5x - 1.5 = -12.5

-11.5x - 1.5 = -12.5

-11.5x = -11

x = 1

Finally, substitute this value of x back into the equation y = 3.25x + 0.75 to find y:

y = 3.25(1) + 0.75

y = 3.5

Therefore, the solution to the system of equations is (1, 3.5).

Answer 2

Assuming you mean > -4.5x - 2y = -12.5; 3.25x - y = -0.75 as a system of equations we shall solve.
So solve 3.25x − y = −0.75 for y
3.25x − y + −3.25x = −0.75 + −3.25x (Note we are adding -3.25x to both sides)
−y = −3.25x − 0.75
Now divide both sides by -1.

`(-y)/(-1) =(-3.25 - 0.75)/(-1) \ \textgreater \ y = 3.25x + 0.75`
Now we must substitute 3.25x + 0.75 for y in −4.5x − 2y = −12.5
-4.5x - 2y = -12.5
-4.5x - 2(3.25x + 0.75) = -12.5
Now simplify both sides.
-11x - 1.5 = -12.5
Then add 1.5 to both sides.
-11x - 1.5 + 1.5 = -12.5 + 1.5
-11x = -11
Then divide both sides by -11.

`(-11x)/(-11) =(-11)/(-11) > x = 1`
Now we need to substitute 1 for x in y = 3.25x + 0.75.
y = 3.25x + 0.75y = (3.25)(1) + 0.75
When we simplify both sides we get y = 4
So we get x = 1 and y = 4. Hope this helps!