A system of linear equations is shown below. 4
x
+
y
=
1

8
x
−
3
y
=
12

What is the solution to the system or equations?

Given 4x + y = 1 (equation 1) and 8x - 3y = 12 (equation 2)

Using the substitution method:

Equation 1: Subtract 4x from both sides to isolate y:

4x - 4x + y = -4x + 1

y = -4x + 1

Substitute the value of y into equation 2:

8x - 3y = 12
8x - 3(-4x + 1) = 12
8x + 12x - 3 = 12

Combine like terms:
20x - 3 = 12

Add 3 to both sides:

20x - 3 + 3 = 12 + 3
20x = 15

Divide both sides by 20 to solve for x:

20x/20 = 15/20
x = 15/20 or ¾

Substitute the value of x = ¾ into Equation 1 to solve for y:

4x + y = 1
4(¾) + y = 1
3 + y = 1

Subtract 3 from both sides to isolate y:
3 - 3 + y = 1 - 3
y = -2

Therefore, the solution of the given systems of linear equations is: x = ¾, y = -2 or (¾, -2).

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