7¡Á - 2y = 15 3¡Á + 4y = 15
To solve this system of equations, one common method is to use the method of elimination. Here are the steps:
Step 1: Multiply both sides of the first equation by 3 to eliminate the 3¡Á term:
21¡Á - 6y = 45
Step 2: Multiply both sides of the second equation by 7 to eliminate the 7¡Á term:
21¡Á + 28y = 105
Step 3: Now, subtract the first equation from the second equation to eliminate the 21¡Á terms:
(21¡Á + 28y) - (21¡Á - 6y) = 105 - 45
Simplifying, we get:
21¡Á + 28y - 21¡Á + 6y = 60
Step 4: Combine like terms on both sides:
34y = 60
Step 5: Divide both sides of the equation by 34 to solve for y:
y = 60/34
Simplifying the fraction, we get y ≈ 1.76 (rounded to two decimal places).
Step 6: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
7¡Á - 2y = 15
7¡Á - 2(1.76) = 15
7¡Á - 3.52 = 15
7¡Á = 15 + 3.52
7¡Á = 18.52
Step 7: Divide both sides of the equation by 7 to solve for x:
x = 18.52 / 7
Simplifying, we get x ≈ 2.64 (rounded to two decimal places).
Therefore, the solution to the system of equations is x ≈ 2.64 and y ≈ 1.76.