Answer:
x = -1, and y = -9
Step-by-step explanation:
This is done by solving one of the two equations for x or y, then substituting it in place of that variable in the other equation.
Since y is already clearly defined in the second equation let's go with that:
[tex]Given\ 7x - 3y = 20,\ and\ y = 5x - 4[/tex]
[tex]7x - 3(5x - 4) = 20[/tex]
[tex]7x - 15x + 12 = 20[/tex]
[tex]7x - 15x = 20 - 12[/tex]
[tex]-8x = 8[/tex]
[tex]x = -1[/tex]
Now we can replace x in the equation for y with -1:
[tex]y = 5(-1) - 4[/tex]
[tex]y = -5 - 4[/tex]
[tex]y = -9[/tex]
To make sure our answers are correct, let's substitute them into the original equations:
[tex](-9) = 5(-1) - 4\\-9 = -5 - 4\\-9 = -9[/tex]
Good, let's test the other equation
[tex]7(-1) - 3(-9) = 20\\-7 - (-27) = 20\\-7 + 27 = 20\\20 = 20[/tex]
So we know that our answer is correct.
