Answer:
[tex]\boxed {\boxed {\sf (5,-4)}}[/tex]
Step-by-step explanation:
We are given the equations:
[tex]3x+2y=7 \\y=3x-19[/tex]
Since we know what y is equal to, we can substitute that expression in for y in the first equation.
[tex]3x+2(3x-19)=7[/tex]
Distribute the 2. Multiply each term inside the parentheses by 2.
[tex]3x+(2*3x)+ (2*-19)=7[/tex]
[tex]3x+6x+-38= 7[/tex]
Combine the like terms (the terms with variables).
[tex]9x-38=7[/tex]
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.
[tex]9x-38+38=7+38 \\9x=7+38\\9x=45[/tex]
Now x is being multiplied by 9. The inverse of multiplication is division. Divide both sides by 5.
[tex]9x/9=45/9\\x=45/9\\x=5[/tex]
Now we know what x is equal to and can substitute the value into the second equation.
[tex]y=3x-19[/tex]
[tex]y=3(5)-19[/tex]
Multiply.
[tex]y=15-19[/tex]
Subtract.
[tex]y= -4[/tex]
Coordinate points are written as (x,y). Therefore, the solution is (5, -4).
