y = 40 + (x - 600)*0.35
y = 50 + (x - 600)*0.10
what are the steps to get the answer
40 + ( x - 600 ) * 0.35 = 50 + ( x - 600 ) * 0.1
40 + 0.35 x - 600 * 0.35 = 50 + 0.1 x - 600 * 0.1
40 + 0.35 x - 210 = 50 + 0.1 x - 60
0.35 x - 170 = 0.1 x - 10
0.35 x - 0. 1 x = - 10 + 170
0.25 x = 160 Divide both sides by 0.25
x = 160 / 0.25 = 160 * 4
x = 640
Remark :
Dividing by 0.25 is equal to multiply by 4 becouse
1 / 0.25 = 4
To solve the system of equations:
1. Start with the given equations:
y = 40 + (x - 600)*0.35
y = 50 + (x - 600)*0.10
2. Since both equations are set equal to y, you can set the right-hand sides of the equations equal to each other:
40 + (x - 600)*0.35 = 50 + (x - 600)*0.10
3. Distribute the multiplication on both sides:
40 + 0.35x - 210 + 210*0.35 = 50 + 0.10x - 60 + 60*0.10
4. Simplify both sides of the equation:
0.35x - 170 + 210*0.35 = 0.10x - 10 + 60*0.10
5. Combine like terms on both sides:
0.35x - 170 + 73.5 = 0.10x - 10 + 6
6. Simplify further:
0.35x - 96.5 = 0.10x - 4
7. Arrange the equation so that all terms with x are on one side and the constant terms are on the other side:
0.35x - 0.10x = -4 + 96.5
8. Combine like terms on both sides:
0.25x = 92.5
9. Divide both sides of the equation by 0.25 to solve for x:
x = 92.5/0.25
10. Calculate the value of x:
x = 370
11. Substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
y = 40 + (370 - 600)*0.35
y = 40 + (-230)*0.35
y = 40 - 80.5
y = -40.5
Therefore, the solution to the system of equations is x = 370 and y = -40.5.