Question

3x+2y=7 y=3x-19 could someone show me a step by step for this equation for substitution

Answer 1

x=5,y=-4

Explanation:

1. [
   `(3x+2y=7)/(y=3x-19)`]
2. [3x+2(3x-19)=7]
3. [9x-38=7]
4. y=3 · 5 - 19
5. x=5,y=-4

Answer 2

`\boxed {\boxed {\sf (5,-4)}}`

Explanation:

We are given the equations:

`3x+2y=7 \\y=3x-19`

Since we know what y is equal to, we can substitute that expression in for y in the first equation.

`3x+2(3x-19)=7`

Distribute the 2. Multiply each term inside the parentheses by 2.

`3x+(2*3x)+ (2*-19)=7`

`3x+6x+-38= 7`

Combine the like terms (the terms with variables).

`9x-38=7`

Since we are solving for x, we must isolate the variable. 38 is being subtracted and the inverse of subtraction is addition. Add 38 to both sides.

`9x-38+38=7+38 \\9x=7+38\\9x=45`

Now x is being multiplied by 9. The inverse of multiplication is division. Divide both sides by 5.

`9x/9=45/9\\x=45/9\\x=5`

Now we know what x is equal to and can substitute the value into the second equation.

`y=3x-19`

`y=3(5)-19`

Multiply.

`y=15-19`

Subtract.

`y= -4`

Coordinate points are written as (x,y). Therefore, the solution is (5, -4).