Find the point of intercept of the lines 2.1y - 3.2x =1.3 and 1.1x +3.1y=9.8. consider significant digits.
let's use substitution.
From the first equation, y = (3.2x+1.3)/2.1
Plug that into the 2nd equation and you can find x:
1.1x + 3.1*(3.2x+1.3)/2.1 = 9.8
Then use that to find y.
To find the point of intercept of two lines, we need to solve the given system of equations. In this case, we have the equations:
1) 2.1y - 3.2x = 1.3
2) 1.1x + 3.1y = 9.8
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve equation (1) for y:
2.1y = 1.3 + 3.2x
Divide both sides by 2.1:
y = (1.3 + 3.2x) / 2.1
Step 2: Substitute the value of y from equation (1) into equation (2):
1.1x + 3.1((1.3 + 3.2x) / 2.1) = 9.8
Step 3: Solve equation (2) for x:
Multiply both sides by 2.1 to eliminate the fraction:
2.31x + 6.51 + 6.72x = 20.58
Combine like terms:
8.03x + 6.51 = 20.58
Subtract 6.51 from both sides:
8.03x = 14.07
Divide both sides by 8.03:
x = 1.75
Step 4: Substitute the value of x into equation (1) to find y:
2.1y - 3.2(1.75) = 1.3
2.1y - 5.6 = 1.3
2.1y = 1.3 + 5.6
2.1y = 6.9
Divide both sides by 2.1:
y = 3.29
Therefore, the point of intercept is (x, y) = (1.75, 3.29) considering significant digits.