Here are the problems that we would like to study:
Here are two using the substatution method:
y = 2x
y = x + 5
Step 1. y = 2x
y = x + 5 Both equations are solved for y.
Step 2. y = x+5
2x = x + 5 Substitute 2x for y in the second equation.
Step 3. -x___-x
x = 5 Now solve this equation for x. Subtract x from
both sides to combine like terms.
Step 4. y = 2x
y = 2 (5) Write one of the original equations substitute 5 for x
y = 10
Step 5. (5,10) Write the solution as an ordered pair.
2x + y = 5
y = x - 4
Step 1. y = x - 4 The second equation is too solve for x
Step 2. 2x + y = 5 Write the first equation.
2x + (x - 4) = 5 Substitute x -4 for y in the first equation.
Step 3. 3x - 4 = 5 Simplify and solve for x.
+4 +4 Add 4 to both sides.
3x = 9
3x = 9
3x = 9 Divide both sides by 3.
3 3
x = 3
Step 4. y = x - 4 Write one of the original equations.
y = 3 - 4 Substitute 3 for x.
y = -1
Step 5. (3,-1) Write the solution as an ordered pair.
y = 2x
y = x + 5
Step 1. y = 2x
y = x + 5 Both equations are solved for y.
Step 2. y = x+5
2x = x + 5 Substitute 2x for y in the second equation.
Step 3. -x___-x
x = 5 Now solve this equation for x. Subtract x from
both sides to combine like terms.
Step 4. y = 2x
y = 2 (5) Write one of the original equations substitute 5 for x
y = 10
Step 5. (5,10) Write the solution as an ordered pair.
2x + y = 5
y = x - 4
Step 1. y = x - 4 The second equation is too solve for x
Step 2. 2x + y = 5 Write the first equation.
2x + (x - 4) = 5 Substitute x -4 for y in the first equation.
Step 3. 3x - 4 = 5 Simplify and solve for x.
+4 +4 Add 4 to both sides.
3x = 9
3x = 9
3x = 9 Divide both sides by 3.
3 3
x = 3
Step 4. y = x - 4 Write one of the original equations.
y = 3 - 4 Substitute 3 for x.
y = -1
Step 5. (3,-1) Write the solution as an ordered pair.