The correct answer for question 1 is A. 3x + 8y = $70; 8x + 3y = $115.
To solve the system of equations, you can use the method of substitution or elimination.
Using the method of substitution:
1. Solve one equation for x or y.
For example, solve the first equation for x: x = ($70 - 8y)/3.
2. Substitute the expression for x into the second equation.
Substitute ($70 - 8y)/3 for x in the second equation: 8(($70 - 8y)/3) + 3y = $115.
3. Solve the resulting equation for y.
24(($70 - 8y)/3) + 3y = $115.
4. Solve for y: 56 - 64y/3 + 3y = $115.
56 - 64y + 9y/3 = $115.
5. Simplify and solve for y: 56 - 24y + 3y = $115.
32 - 21y = $115.
-21y = $115 - $32.
-21y = $83.
y = $83/(-21).
y = -$3.
6. Substitute the value of y=-$3 into one of the original equations to solve for x.
Using the first equation: 3x + 8(-$3) = $70.
3x - 24 = $70.
3x = $70 + $24.
3x = $94.
x = $94/3.
x = $31.33.
Therefore, the cost of each table (x) is approximately $31.33 and the cost of each chair (y) is -$3.
The correct answer for question 2 is D. x = $12; y = $3.
Solving a Linear System
A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.
Question 1
Which system of linear equations could be used to find the cost of each table (x) and the cost of each chair (y)?
Responses
A 3x + 8y = $70; 8x + 3y = $1153x + 8y = $70; 8x + 3y = $115
B 5x + 8y = $115; 3x + 5y = $705x + 8y = $115; 3x + 5y = $70
C 5x + 8y = $115; 2x − 5y = $705x + 8y = $115; 2x − 5y = $70
D 8x + 5y = $115; 5x + 3y = $708x + 5y = $115; 5x + 3y = $70
Question 2
Determine the cost of each table (x) and the cost of each chair (y).
Responses
A x = $15; y = $5x = $15; y = $5
B x = $10; y = $5x = $10; y = $5
C x = $5; y = $10x = $5; y = $10
D x = $12; y = $3
1 answer