Quiz about Solve Systems Using Substitution

Question 1

7. Solve the system of equations using substitution method: 4x + y = 23, y - x = 3

Accepted Answer

x = 4, y = 7

Answer

x = 3, y = 6

Answer

x = 6, y = 9

Answer

x = 5, y = 8

Question 2

Determine the values of x and y by using substitution method for the system of equations: 6x + 2y = 44, y = 3x - 2

Accepted Answer

x = 4, y = 10

Answer

x = 8, y = 20

Answer

x = 5, y = 12

Answer

x = 2, y = 6

Question 3

10. Solve the following system of equations using substitution method: 3x + 2y = 29, y = 2x - 3

Accepted Answer

x = 5, y = 7

Answer

x = 2, y = 5

Answer

x = 6, y = 8

Answer

x = 3, y = 4

Question 4

Solve this system of equations:
2x + 2y = 12
y = 2x

Accepted Answer

(2, 4)

Answer

(2, 2)

Answer

(3, 6)

Answer

(4, 2)

Question 5

Solve this system using substitution:
3x + 4y = 15
y = 3

Accepted Answer

(1, 3)

Answer

(3, 1)

Answer

(4, 3)

Answer

(3, 4)

Question 6

Jess correctly graphs a system of equations on her calculator but sees only one line as a result. What does this mean?

Accepted Answer

The system has infinite solutions

Answer

The system has one solution

Answer

The system has no solutions

Answer

The calculator's broken

Question 7

Which of the following could be a first step when solving using substitution for the given system of equations?

Accepted Answer

$$x=\frac{3}{2}-\frac{3}{2}y$$

Accepted Answer

$$y=1-\frac{2}{3}x$$

Accepted Answer

$$x=-2+\frac{5}{3}y$$

Answer

$$x=\frac{6}{5}+\frac{3}{5}y$$

Answer

$$x=2-\frac{5}{3}y$$

Question 8

Given the following sytem of linear equations, If I solved the second equation for x, which would be correct steps for solving the system using substitution?

Accepted Answer

$$\frac{19}{3}y=7$$

Accepted Answer

$$-4+\frac{10}{3}y+\frac{9}{3}y=3$$

Accepted Answer

$$-3x+5\left(\frac{21}{19}\right)=6$$

Answer

$$2x+3\left(-2+\frac{5}{3}y\right)=3$$

Answer

$$2\left(\frac{21}{19}\right)+3y=3$$

Question 9

What is the initial step when using the Substitution method to solve a system of equations?

Accepted Answer

Ensure one equation is isolated for a variable.

Answer

Ensure both equations are in point-slope form.

Answer

Ensure both equations are in standard form.

Question 10

Two students attempted to solve the following system of equations using substitution:
$$y=2x+3$$

$$3x-y=7$$

To start solving the problem, Student C wrote $$3x-\left(2x+3\right)=7$$ and Student D wrote $$3\left(2x+3\right)-y=7.$$

Which student made the correct substitution?

Accepted Answer

Student C

Answer

Student D

Answer

Neither student made the correct substitution

Question 11

What is the solution to the following system:

^{y = 5x}

^{3x + y = 24}

Accepted Answer

(3, 15)

Answer

(15, 3)

Answer

(3, 5)

Answer

(5, 3)

Question 12

Which option shows the CORRECT substitution for this system? $$x+2y=2$$ and $$x=-4y+2$$

Accepted Answer

$$\left(-4y+2\right)+2y=2$$

Answer

$$x+2y=-4y+2$$

Answer

$$x+2\left(-4y+2\right)=2$$

Question 13

What is the solution to the system: $$y = 3x + 7$$ and $$2y - 6x = 14$$ .

Accepted Answer

Infinite Solutions

Answer

No Solution

Answer

(0,7)

Answer

(-2.33,0)

Solve Systems Using Substitution

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