We need to continue working on simultaneous equations. Here are the bullet points of the 3 methods for solving 2 equations in the same problem. Read and then solve the problems at the bottom correctly:
GRAPHING:
Put each equation into the form y = mx + b, then plot b on the y-axis, then move up (or down) and over whatever amount is dictated by the slope.
ex. 2x + y = 10 & x – 3y = 9
1st equation: subtract 2x from both sides to get y = -2x + 10. b = 10 and slope (m) = -2.
2nd equation: subtract x from both sides, then divide by -3 (because it is the coefficient of y) to get y = 1/3 x – 3. b = -3 and slope (m) is 1/3.
SUBSTITUTION: Get each equation into y = mx + b format and set them equal to eachother:
ex. 4y = 16 – 8x and x + y = 22
Take first equation and divide by 4, take second equation and subtract x from both sides. You now have
y = 4 – 2x and y = 22 + x
Set them equal to eachother: 4 – 2x = 22 + x. Solve this easy equation for x…it turns out to be -6. then plug -6 into EITHER original equation and you should get y = 16.
ELIMINATION:
This is where you stack the equations and add or subtract an entire equation from the other one to get rid of one of the 2 variables. It does not matter which one is on top, it does not matter whether you eliminate y or x.
ex. 2x + 5y = 12 and x = 3 – y
rearrange the 2nd one to match the positioning of the terms in the first one. You can accomplish this simply by adding y to both sides:
x = 3 – y becomes x + y = 3
Now stack ‘em
2x + 5y = 12
x + y = 3
double the 2nd equation
2x + 5y = 12
2x + 2y = 6
subtract, and you get
3y = 6 … or y = 2 plug that in to either equation and get x.
OK Now use EACH of these methods to solve the following two exercises:
1) 4x – y = 12 and 2y + x = -6
2) y = 3x – 16 and x – y = 6
THESE ARE DUE FRIDAY. IF EVERYONE DOES THEM I WILL NOT ASSIGN WEEKEND HOMEWORK.
