Solve the system of two equations using substitution. y=2+3x 4x−3y=−16

Answer 1

We can solve the system of equations using substitution by solving one equation for a variable and substituting that expression into the other equation.

First, let's solve the first equation, y = 2 + 3x, for y:
y = 2 + 3x.

Next, substitute this expression for y in the second equation, 4x - 3y = -16:
4x - 3(2 + 3x) = -16.

Expanding the equation:
4x - 6 - 9x = -16.

Combine like terms:
-5x - 6 = -16.

Now, isolate x:
-5x = -16 + 6,
-5x = -10,
x = 2.

Now that we have found x, substitute this value into the first equation to find y:
y = 2 + 3(2),
y = 2 + 6,
y = 8.

Therefore, the solution to the system of equations is x = 2 and y = 8.

Answer 2

what would that answer look like as a ratio

Answer 3

To write the solution as a ratio, we can express the values of x and y as a fraction:

x = 2 can be written as x/y = 2/1,
y = 8 can be written as x/y = 1/8.

So, the ratio of x to y is 2/1 or simplified as x:y = 2:1, and the ratio of y to x is 1/8 or simplified as y:x = 1:8.

Answer 4

what would the answer look like as a coordinate

Answer 5

The solution to the system of equations, in coordinate form, is (2, 8). This means that the value of x is 2 and the value of y is 8. Thus, the coordinates represent a point on the coordinate plane.