If you substitute the values x = − 5 and y = 2 into the second equation, you get a false statement: 2(2) − 10 = 2( − 5). Substituting these values into either equation results in a true statement: 2(3) = − 2 + 8, and 2(3) − 10 = 2( − 2). The correct answer is x = − 2, y = 3.Ĭorrect. Then substitute 2 y − 8 in for x in the second equation, and solve for y. To solve this system, try rewriting the first equation as x = 2 y − 8. If you substitute the values x = − 3 and y = 2 into the first equation, you get a false statement: 2(2) = − 3 + 9. Sometimes you may have to rewrite one of the equations in terms of one of the variables first before you can substitute. This allowed us to quickly substitute that value into the other equation and solve for one of the unknowns. In the examples above, one of the equations was already given to us in terms of the variable x or y. To find y, substitute this value for x back into one of the original equations.Ĭheck the solution x = −2, y = 0 by substituting them into each of the original equations. Substitute 3 x + 6 for y into the second equation. The first equation tells you how to express y in terms of x, so it makes sense to substitute 3 x + 6 into the second equation for y. Let’s look at another example whose substitution involves the distributive property.Ĭhoose an equation to use for the substitution. The ordered pair (4, − 1) does work for both equations, so you know that it is a solution to the system as well. Remember, a solution to a system of equations must be a solution to each of the equations within the system. X = 4, y = −1 by substituting these values into each of the original equations. To now find x, substitute this value for y into either equation and solve for x. Equation B tells us that x = y + 5, so it makes sense to substitute that y + 5 into Equation A for x. The goal of the substitution method is to rewrite one of the equations in terms of a single variable.
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