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Make Your Own Math Problem!
Systems of Equations
Instructions
Part 1: Find the Slope.
1. Find 2 points.
2. Using the coordinates, substitute into the equation
3. Simplify the resulting fraction. This is the slope.
Example
1. (1, 5)
(3, 8)
2. 8 - 5 = 3
3 -1
2
3. m = 3/2
Part 2: Find the y-intercept.
1. You know the slope. m = (the answer to part 1)
1. m = 3/2
2. You know a point. (x, y)
2. (1, 5)
3. Substitute the known values into the equation y = mx + b 3. 5 = (3/2)(1) + b
and solve for b.
5 = 3/2 + b
4. b is the y-intercept.
5 – 3/2 = 3-2 – 3/2 +b subtract 3/2
from both sides
4. 7/2 or 3.5 = b
Part 3: Write an equation in slope intercept form.
1. You know the slope. (m from Part 1)
2. You know the y-intercept. (b from Part 2)
3. Substitute m and b into the slope-intercept equation. y =
mx + b
Part 4: Write an equation in standard form.
1. Start with your slope-intercept equation. y = mx + b
2. The goal is to get it into standard form: Ax + By = C.
3. First, subtract mx from both sides. y – mx = b
4. Rearrange the terms. –mx + y = b
5. Remember, in standard form the coefficient of x must be
a positive, whole number.
a. If needed, multiply both sides of the equation by
the denominator of the coefficient of x.
b. Then, if needed, multiply both sides of the
equation by -1 to make the coefficient of x
positive.
6. The final equation should be in standard form: Ax + By =
C, where A is a positive, whole number.
1. m = 3/2
2. b = 3.5
3. y = 3/2x + 3.5
1. y = 3/2x + 3.5
2.
3. y – 3/2x = 3/2x – 3/2x +3.5
4. -3/2x + y = 3.5
5.
a. 2(-3/2x + y) = 2(3.5)
-3x + 2y = 7
b. -1(-3x + 2y) = -1(7)
3x -2y = -7
6. 3x -2y = -7
Part 5: Write the system of equations.
1. Remember, the difference between a list of equations
and a system of equations, is that equations in a system
are all graphed on the same coordinate plane. To
denote this, use a bracket {
a.
{
1.
{
 Line A
 Line B
b. (You may use either the slope-intercept form or
standard form for each equation.)
Part 6: Find the solution to the system of equations.
1. The solution is the point where the two lines intersect,
so it will be written (x,y).
2. You have two equations, one for line A and one for line
B.
y = mx + b line A
y = mx + b line B
3. Since they are both set equal to y, they can also be set
equal to each other.
mx + b = mx + b
4. Solve for x.
1.
2. y = 3/2x + 3.5
y = -2x + 1
3. 3/2x + 3.5 = -2x + 1
4. 3/2x + 3.5 – 3.5 = -2x + 1 -3.5
(subtract 3.5 from both sides)
3/2x = -2x – 2.5
3/2x + 2x = -2x + 2x – 2.5
(add 2x to both sides)
7/2x = -2.5
(2/7)(7/2x) = -2.5(2/7)
Multiply both sides by
the reciprocal of 7/2.
-2.5 = -5/2 converted to a
fraction.
-5 2 = -5
2 7 7
x = -5/7
5. This gives you the x value for the solution.
6. Substitute that x value into one of the equations from #2
and solve for y.
7. This gives you the y value for the solution.
8. Write the solution as (x, y).
5.
6. y = 3/2(-5/7) + 3.5
y = -15/14 + 7/2  converted 3.5
to a fraction
y = -15/14 + 49/14
y = 34/14
y = 17/7 or 2 3/7
7. y = 17/7
8. (-5/7, 17/7)