Question

1. a system of equations is shown.

$x + y = 7$
$x - y = 3$
which of the following would be the best first step to take to solve this system by elimination?
a add the equations to eliminate the x variables.
b subtract the equations to eliminate the y variables.
c add the equations to eliminate the y variables.
d this system cannot be solved by elimination.

1. solve the system of equations using the elimination method.

$x + y = 7$
$x - y = 3$

1. a system of equations is shown.

$x + 2y = 12$
$2x + 2y = 8$
which of the following would be the best first step to take to solve this system by elimination?
a subtract the equations to eliminate the x variables.
b add the equations to eliminate the y variables.
c subtract the equations to eliminate the y variables.
d this system cannot be solved by elimination.

1. solve the system of equations using the elimination method.

$x + 2y = 12$
$2x + 2y = 8$

1. a system of equations is shown.

$2x + 5y = -3$
$2x + 2y = 6$
which of the following would be the best first step to take to solve this system by elimination?
a subtract the equations to eliminate the x variables.
b add the equations to eliminate the y variables.
c subtract the equations to eliminate the y variables.
d this system cannot be solved by elimination.

1. solve the system of equations using the elimination method.

$2x + 5y = -3$
$2x + 2y = 6$

mrs. casias math 2024 ©

Explanation:

Question 1

Step1: Analyze the system of equations

The system is \( x + y = 7 \) and \( x - y = 3 \). We want to eliminate a variable. The coefficients of \( y \) are \( 1 \) and \( -1 \).

Step2: Check elimination by addition

If we add the two equations: \( (x + y)+(x - y)=7 + 3 \), which simplifies to \( 2x=10 \). This eliminates the \( y \)-variables. Now check the options:

• Option A: Adding would not eliminate \( x \) (coefficients of \( x \) are both \( 1 \), adding gives \( 2x \), not elimination).
• Option B: Subtracting to eliminate \( y \) is not necessary, adding works.
• Option C: Adding eliminates \( y \) (as shown above), this is correct.
• Option D: The system can be solved by elimination.

Step1: Write the system of equations

The system is \( x + y = 7 \) and \( x - y = 3 \). We use elimination by adding the equations.

Step2: Add the two equations

\( (x + y)+(x - y)=7 + 3 \)
Simplify the left - hand side: \( x + y+x - y = 2x \)
Simplify the right - hand side: \( 7 + 3=10 \)
So we have \( 2x = 10 \)

Step3: Solve for x

Divide both sides of \( 2x = 10 \) by \( 2 \): \( x=\frac{10}{2}=5 \)

Step4: Substitute x = 5 into one of the original equations

Substitute \( x = 5 \) into \( x + y = 7 \): \( 5 + y = 7 \)
Subtract \( 5 \) from both sides: \( y=7 - 5 = 2 \)

Step1: Analyze the system of equations

The system is \( x + 2y=12 \) and \( 2x + 2y = 8 \). The coefficients of \( y \) in both equations are \( 2 \).

Step2: Check elimination methods

If we subtract the two equations: \( (x + 2y)-(2x + 2y)=12 - 8 \)
Simplify the left - hand side: \( x+2y - 2x - 2y=-x \)
Simplify the right - hand side: \( 12 - 8 = 4 \)
This eliminates the \( y \)-variables. Now check the options:

• Option A: Subtracting to eliminate \( x \) is incorrect (coefficients of \( x \) are \( 1 \) and \( 2 \), subtracting won't eliminate \( x \)).
• Option B: Adding the equations will give \( 3x + 4y=20 \), which does not eliminate \( y \).
• Option C: Subtracting the equations eliminates \( y \) (as shown above), this is correct.
• Option D: The system can be solved by elimination.

Answer:

C. Add the equations to eliminate the y variables.

Question 2