Solving Systems of Equations Algebraically Peter Gibby Systems

Solving Systems of Equations Algebraically Peter Gibby

Systems of Equations • A system of equations is when we use 2 or more equations each with multiple variables to determine each value. • We know that the pairs are related to each other, so the x is the same value for each equation and the y is the same, otherwise we couldn’t solve them.

Solving Systems of Equations • To solve a system of equations, we use the equations together to alter one and remove a variable. We can either do this by adding the equations together or substitution. • Lets look at a simple system of equation and do both: – 6 x-3 y=15 – 2 x+3 y=17

Adding Equations Together 6 x-3 y=15 2 x+3 y=17 • We know that we can alter equations as long as we do the same thing to both sides so that it only looks different. Well if 2 x+3 y=17, lets add 17 to both sides(or in other terms: 2 x+3 y to one and 17 to the other) 6 x-3 y+2 x+3 y=15+17 8 x+0 y=32 X=4

Next Step 6 x-3 y=15 2 x+3 y=17 X=4 • These are three equations we have now, but to solve a system of equations, we need both the x and the y value. So we plug 4 as x into one of the equations. 6(4)-3 y=15 24 -3 y=15 9=3 y Y=3 the answers are y=3 and x=4 then!

Substitution • The other method is called substitution. • We substitute one value by manipulating an equation so we know what the variable equals in terms of the other. • 6 x-3 y=15 2 x+3 y=17 6 x-15=3 y 2 x-5=y 2 x+3(2 x-5)=17 2 x+6 x-15=17 8 x=32 x=4 then plugging in: y=3