Question

4a2+2b=10,-2a + 7b=9,-7x+2y=-3,-4x+5y=-4

Answer 1

4a*2+2b=10
8a+2d=10
8a=10-2b
a=5/4-1/4b
a=5/4-1/4b

Answer 2

To solve the system of equations, we'll use the method of substitution or elimination. Let's go through the steps:

1. 4a + 2b = 10 ...........(Equation 1)
2. -2a + 7b = 9 ...........(Equation 2)
3. -7x + 2y = -3 ..........(Equation 3)
4. -4x + 5y = -4 ..........(Equation 4)

We'll solve the first pair of equations (Equation 1 and Equation 2) for 'a' and 'b'.

Step 1: Solve Equation 1 for 'a': 4a = 10 - 2b a = (10 - 2b) / 4 a = 5/2 - (1/2)b

Step 2: Substitute the value of 'a' from Step 1 into Equation 2: -2(5/2 - (1/2)b) + 7b = 9 -5 + b + 7b = 9 6b = 9 + 5 6b = 14 b = 14 / 6 b = 7/3

Step 3: Substitute the value of 'b' from Step 2 into Equation 1 to find 'a': a = 5/2 - (1/2)*(7/3) a = 5/2 - 7/6 a = (15 - 7) / 6 a = 8 / 6 a = 4 / 3

Now, we have found the values of 'a' and 'b': a = 4/3 b = 7/3

Next, we'll solve the second pair of equations (Equation 3 and Equation 4) for 'x' and 'y'.

Step 4: Solve Equation 3 for 'x': -7x = -3 - 2y x = (-3 - 2y) / -7 x = (3 + 2y) / 7

Step 5: Substitute the value of 'x' from Step 4 into Equation 4: -4((3 + 2y) / 7) + 5y = -4 -(12 + 8y) / 7 + 5y = -4 -12 - 8y + 35y = -28 (Multiply both sides by 7 to eliminate the fraction) 27y = -16 y = -16 / 27

Step 6: Substitute the value of 'y' from Step 5 into Equation 3 to find 'x': x = (3 + 2*(-16/27)) / 7 x = (3 - 32/27) / 7 x = (81/27 - 32/27) / 7 x = 49/27 / 7 x = (49/27) * (1/7) x = 49 / 189

Now, we have found the values of 'x' and 'y': x = 49/189 y = -16/27

The solution to the system of equations is: a = 4/3, b = 7/3, x = 49/189, and y = -16/27.