Question

What is the best approximation of the solution to the system to the nearest integer values? (−2, 7) (−2, 6) (6, −2) (7, −2) Graph of a system of linear equations. Equation 1 is 3x minus 4y equals negative 32. Equation 2 is 3x plus 5y equals 24.

Answer 1

(-2,6)

Explanation:

Equation 1 : 3x - 4y = -32

Equation 2 : 3x + 5y = 24

Lets graph both the equations

LEts find x and y intercepts for graphing

Equation 1 : 3x - 4y = -32

To find x intercept , plug in 0 for y

3x - 4(0) = -32

3x= -32 so x = -32/3

x intercept is (-32/3, 0)

to find y intercept plug in 0 for x

3(0) - 4y = -32

-4y =-32

y = 8

y intercept is (0,8)

Equation 2 : 3x + 5y = 24

To find x intercept , plug in 0 for y

3x + 5(0) = 24

3x= 24 so x = 8

x intercept is (8, 0)

to find y intercept plug in 0 for x

3(0) + 5y = 24

5y=24

y = 24/5

y intercept is (0,24/5)

plot the intercepts for each equation and join it by a line

the graph is attached below

Both graphs intersects at (-2.37, 6.2222)

Round the answer to nearest integer

So answer is (-2, 6)