Question

How can I solve this system of linear equation by substitution 3x+y=11 and -2x+y=1

Answer 1

First will make Equation take on the form of y = mx + b. I've cchosen the second Equation:

y = 2x + 1


Now substitute this equation in for y into the other equation and solve:

3x+y = 11
3x+ (2x + 1)=11
5x + 1 = 11
5x = 11 - 1
5x/5= 10/5
x = 2 


You can now plug this x-value back into either equation, and solve for y:

y = 2(x) + 1
y = 2(2) + 1
y = 5

Answer 2

We can answer this question by solving each equation for one variable, and then substituting.

3x + y = 11   Given
y = -3x + 11   Subtract 3x from both sides

This equation is now solved for y. Now, let's do the other equation. Make sure to solve it for the same variable.

-2x + y = 1   Given
y = 2x + 1   Add 2x to both sides

Now, let's set both equations equal to each other, since they both equal y.

2x + 1 = -3x + 11   Set both equations equal to each other
1 = -5x + 11   Subtract 2x from both sides
-10 = -5x   Subtract 11 from both sides
2 = x   Divide both sides by -5

Now, let's substitute x in for one of the equations we found earlier, so that we can find y.

y = 2x + 1   Given
y = (2)(2) + 1   Substitute the x-value, 2
y = 4 + 1   Multiply
y = 5   Add

So, x = 2 and y = 5.

Hope this helps!