What is the solution to this system of equations?
One-fourth x + 1 and one-half y = StartFraction 5 Over 8 EndFraction. Three-fourths x minus 1 and one-half y = 3 and StartFraction 3 Over 8 EndFraction
(4, negative one-fourth)
(4, negative StartFraction 9 Over 16 EndFraction)
no solution
infinitely many solutions

Answer:

4, -1/4

Step-by-step explanation:

I took the test 2021 on edge

The solution to this system of equations is (4, -1/4)

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Given

[tex]\frac{1}{4} x + 1\frac{1}{2} y = \frac{5}{8} \\\frac{1}{4} x + \frac{3}{2} y = \frac{5}{8} \\\\\frac{x +6y}{4} =\frac{5}{8}\\ x+6y = \frac{5}{8} *4 = \frac{5}{2} \\[/tex]

[tex]2x +12y = 5 ........(i)\\\\\frac{3}{4} x - 1\frac{1}{2} y = 3\frac{3}{8} \\\\\frac{3}{4} x - \frac{3}{2} y = \frac{27}{8} \\\\\frac{3x -6y}{4} =\frac{27}{8}\\ 3x-6y = \frac{27}{8} *4 = \frac{27}{2}[/tex]

6x - 12y = 27...(ii)

Adding equation(i) and (ii),

2x + 6x = 5 + 27

=> 8x = 32

=> x = 4

Plug the value of x in equation(i),

2(4) + 12y = 5

8 + 12y = 5

=> 12y = 5 - 8 = -3

=> y = -1/4

Hence, the solution to this system of equations is (x, y) = 4,-1/4

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