Answer:
x = 4, y = 6, or (4, 6)
Step-by-step explanation:
Given the systems of linear equations, y = x + 2, and y = −¼x + 7:
We could use the substitution method to solve for the solutions:
Equation 1: y = x + 2
Equation 2: y = −¼x + 7
Solve for x:
Start by substituting the value of y from Equation 1 into Equation 2:
y = −¼x + 7
x + 2 = −¼x + 7
Subtract 7 from both sides of the equation:
x + 2 − 7 = −¼x + 7 − 7
x − 5 = −¼x
Next, subtract both sides by x:
x − x − 5 = −¼x − x
[tex]\large\sf{-5\:=\:-\frac{5}{4}x}[/tex]
Multiply both sides by -4 to eliminate the fraction:
[tex]\large\sf{-5(-4)\:=\:-\frac{5}{4}x(-4)}[/tex]
20 = 5x
Divide both sides by 5 to solve for x:
[tex]\displaytext\mathsf{\frac{20}{5}\:=\:\frac{5x}{5}}[/tex]
x = 4
Solve for y:
Substitute the value of 4 into Equation 1 to solve for y:
y = x + 2
y = 4 + 2
y = 6
Solution:
Therefore, the solution to the given systems of linear equations is x = 4, y = 6, or (4, 6).
