Question

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

Answer 1

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.
$\frac{-y}{-1} =\frac{-3.25 - 0.75}{-1} \ \textgreater \ y = 3.25x + 0.75$
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.
$\frac{-11x}{-11} =\frac{-11}{-11} > x = 1$
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!

Answer 2

By solving the system using the substitution method, the value of x = 5.5 and the value of y = 18.625

The substitution method is a method of solving simultaneous equations.

In this method, one variable of the first equation is being made the subject in order to solve for the other variable.

GIven that:

-4.5x - 2y =  -12.5       ----- (1)

3.25x - y = -0.75        ----- (2)

From equation (2), let make (y) the subject of the formula:

-y = -0.75 - 3.25x

multiply through by (-)

y = 0.75 - 3.25x

replace the value of (y) into equation (1) to solve for x.

So, we have;

-4.5x - 2y =  -12.5

-4.5x - 2(0.75 -3.25x) =  -12.5

-4.5x - 1.5 + 6.5x = -12.5

-4.5x + 6.5x = -12.5 + 1.5

2.0x = - 11

Divide both sides by 2

$\mathbf{\dfrac{2x}{2x} = \dfrac{-11}{2}}$

x = 5.5

From equation (2), replace the value of x with 5.5 to solve for y

3.25x - y = -0.75

3.25(5.5) - y = -0.75

17.875 - y = -0.75

-y = -0.75 - 17.875

-y = -18.625

y = 18.625

Therefore, we can conclude that by solving the system using the substitution method, the value of x = 5.5 and the value of y = 18.625

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