Solve the simultaneous equation 4*- ay= 19. 2* + 3y = 1
To solve the simultaneous equations 4x - ay = 19 and 2x + 3y = 1, we can use the method of substitution or the method of elimination. Let's solve it using the method of elimination.
Step 1: Multiply both sides of the second equation by 2 to make the coefficients of x in both equations the same. This gives us:
4x - ay = 19
4x + 6y = 2
Step 2: Subtract the first equation from the second equation to eliminate the x terms. This gives us:
(4x + 6y) - (4x - ay) = 2 - 19
4x + 6y - 4x + ay = -17
Step 3: Simplify the equation. The x terms cancel out, leaving us with:
6y + ay = -17
Step 4: Factor out the common term y:
y(6 + a) = -17
Step 5: Divide both sides by (6 + a) to solve for y:
y = -17 / (6 + a)
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's substitute it into the first equation:
4x - a(-17 / (6 + a)) = 19
Step 6: Multiply both sides of the equation by (6 + a) to eliminate the fraction:
(4x)(6 + a) - a(-17) = 19(6 + a)
Step 7: Expand and simplify the equation:
24x + 4ax + 17a = 114 + 19a
Step 8: Combine like terms:
22x + 4ax = 97a + 114
Step 9: Factor out x:
x(22 + 4a) = 97a + 114
Step 10: Divide both sides by (22 + 4a) to solve for x:
x = (97a + 114) / (22 + 4a)
Now you have the values of x and y, expressed in terms of 'a'.