Solving systems by Substitution Warmup 3

Solve the system of equations using substitution:
y = 2x + 5
2x + 2y = 4

• (1, 7)

• (7, 1)

• (2, 9)

• (-1, 3)

Answer explanation

Substituting y in the second equation: 2x + 2(2x + 5) = 4 simplifies to 6x + 10 = 4. Solving gives x = -1. Substituting x back into y = 2(-1) + 5 results in y = 3. Thus, the solution is (-1, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

In 3x + 2y = 10    and    x - 5y = 18, which variable should you isolate first?

• The x in the first equation

• The y in the first equation

• The x in the first equation

• The x in the second equation

Answer explanation

Isolating x in the second equation, x - 5y = 18, is advantageous because it allows for easier substitution into the first equation. This simplifies solving the system of equations effectively.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the system by substitution. 
-5x - 4y = -9
y = 6

• (3, 6)

• (6, -3)

• (-3, 6)

• (6.8, 3)

Answer explanation

Substituting y = 6 into -5x - 4(6) = -9 gives -5x - 24 = -9. Solving for x, we find x = -3. Thus, the solution is (-3, 6), which matches the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

Answer explanation

The first step in the substitution method is to get either variable by itself. This allows you to express one variable in terms of the other, making it easier to substitute into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the system by substitution.
 
5x + 4y= −14
y =  −7x  −  15 

• (-2, -1)

• (1, -2)

• (-2, 1)

• (-1, -2)

Answer explanation

Substituting y = -7x - 15 into 5x + 4y = -14 gives 5x + 4(-7x - 15) = -14. Simplifying leads to -23x - 60 = -14, resulting in x = -2. Substituting x back gives y = -1. Thus, the solution is (-2, -1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Diego scores 11 more points than Travis.  Together they score 21 points.  How many points did each person score?

• Diego: 11,   Travis: 10

• Diego:  10,  Travis:  11

• Diego: 5,  Travis:  16

• Diego:  16, Travis:  5

Answer explanation

Let Travis's score be x. Then Diego's score is x + 11. Together, x + (x + 11) = 21. Solving gives 2x + 11 = 21, so 2x = 10, and x = 5. Thus, Diego scores 16 and Travis scores 5.

Tags

CCSS.2.OA.A.1