This week in math 10 I learned how to solve a system using substitution.  

Example 1: 

y=-2x+4 

7x-2y=-30

To solve this system, we will begin by inputting our y=-2x+4 into our equation 7x-2y=-30 into the place where the y is currently beside the 4. Our equation should now look like this, 7x-2(-2x+4) = -30. Now we can distribute the 4, our equation now looks like this,7x+4x-8=-30. Now we can add the 7x and 4x together to be 11x. We will add 8 to both sides of our equation to remove it from the left and add it to the right side of the equation. Our equation should now look like this, 11x=-22. Now we need to divide both sides of the equation by 11 to isolate x. Now we have found x, x=-2. Now to determine y we can input x=-2 into the place of the x in y=-2x+4, y=-2(-2)+4. Now we will multiply –2 by –2, leaving us with y=4+4, so we now know that y=8 and our coordinates on a graph where the points intersect is (-2,8). 

 

Example 2: 

x + y = -2

This system of equations contains fractions, but we’ll still solve it! We will begin by taking y = x + 12 and inserting it into the place of the y of the other equation, x– x+ 12 = –2. Now we need to subtract x – x from each other, but to do that we must first make sure their denominators are the same. To make their denominators equal we will multiply each fraction by the other denominator, (4) and (3). Now were left with x x Now we can subtract the numerators (number on the top of the fraction). We’re left with, x + 12 = -2. Now we can subtract negative twelve from both sides of the equation leaving us with x = -14. We’re now going to multiply both sides of the equation by –12 to remove the negative sign and fraction from the variable (x), 5x = 168. Now we will divide both if these numbers by 5 to isolate x. X = 33.6. Now we need to determine our y intercept, we can do this by inserting x = 33.6 into the place of the x in this equation, y = -3/4 x + 12 becomes y = (33.6) + 12. We will multiply (33.6) = 25.2. Now our equation should look like this, y = -25.2 + 12. Now we just need to add the – 25.2 and 12. Y = -13.2. Our coordinates are, (33.6, -13.2)